Mathematics Middle School

How to factor a polynomial when the leading coefficient isn't 1

Answers

Answer 1
You cant... The leading coefficient has to be a whole number, bigger than one
Answer 2

Final answer:

To factor a polynomial with a leading coefficient that isn't 1, use the ac method or factoring by grouping, identify common factors, and check your work by expanding the factors.

Explanation:

When factoring a polynomial with a leading coefficient that isn't 1, you should consider each term, and factor out any common factors first. If the polynomial is a quadratic, for instance, with a leading coefficient greater than 1, you can use techniques such as the ac method or factoring by grouping. The ac method involves finding two numbers which multiply to give you the product of the leading coefficient and the constant term, and add up to the middle term's coefficient. Once you have these numbers, you can rewrite the middle term and then factor by grouping.

Step-by-Step Explanation

Identify the leading coefficient, the constant term, and the middle term's coefficient.Find two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle term's coefficient.Rewrite the middle term using the two numbers found in step 2, splitting it into two terms.Factor by grouping, which involves pairing off the terms in such a way that they have a common factor, and then factoring out the greatest common factor from each pair.If you have factored correctly, you should be able to factor out an additional term from the resulting expression, resulting in a factored polynomial.Simplify further if possible, and check your answer by expanding the factors to ensure you get the original polynomial.

Related Questions

jenny borrowed $500 for 5 years at 4% interest compounded annually. what is the total amount she will have paid when she pays off the loan?

Answers

Use the formula for compound interest,  
  
[tex]A=P(1+ \frac{r}{n})^{nt} [/tex]  
  
Where P is the starting amount (500$), r is the rate of interest (0.04), n is the number of times the interest is compounded per unit (1 per year), and t is the amount of time it is compounded (5 years).  
  
Now, plug it into the formula:  
  
[tex]A=500(1+ \frac{0.04}{1})^{5}[/tex]  
  
Do the math, and your answer is she must pay 608.32$ when she pays her debts.

The scores of several classmates on a language arts test are shown below: 86 points 87 points 87 points 94 points 95 points 82 points 78 points 89 points 80 points 84 points What is the median score for these students?

Answers

78,80,82,84,86,87,87,89,94,95
86+87/2 = 86.5

Answer:

78,80,82,84,86,87,87,89,94,95

86+87/2 = 86.5

Step-by-step explanation:

Which of the fractions shown has the greatest value?

2/4

4/7

1/3

4/9

Answers

4/7 has the greatest value; it is .57
1/2= .5
1/3=.33
4/9 = .44

Answer:

4/7 has the greatest value; it is .57

Step-by-step explanation:

1/2x =20

Pls help
I need answer in like a minute

Answers

if ya meant like [tex]\frac{1}{2}x=20[/tex]
multiply both sides by 2/1 to get x=40

if ya meant like [tex]\frac{1}{2x}=20[/tex]
multiply both sides by x and divide both sides by 20 to get [tex]x=\frac{1}{40}[/tex]

depends which one it is

A bag has 6 yellow marbles and 6 brown marbles. Half of the brown marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a brown, glass marble?

Write your answer as a fraction in simplest form.

Answers

total = 12 marbles
6 brown marbles but half of the brown marbles are made of glass
so brown and made of glass = 3
probability that it is a brown, glass marble = 3/12 = 1/4

answer
1/4

complete the point slope equation of line through (1,-1) and (5,2) use exact numbers

y-(-1)=

Answers

(1,-1)(5,2)
slope = (2 - (-1) / (5 - 1) = 3/4

there will be 2 point slope answers for this..
y - y1 = m(x - x1)
slope(m) = 3/4
(1,-1)...x1 = 1 and y1 = -1
sub
y - (-1) = 3/4(x - 1)
y + 1 = 3/4(x - 1) <=== this is one of them

y - y1 = m(x - x1)
slope(m) = 3/4
(5,2)...x1 = 5 and y1 = 2
sub
y - 2 = 3/4(x - 5) <== here is the other one 


The point - slope equation of line passing through points (1, -1) and (5, 2) is (y + 1) = (3/4)(x - 1).

What is the general equation of a Straight line?

The general equation of a straight line is -

y = mx + c[m] → is slope of line.[c] → is the y - intercept.

Other possible equations of lines are -

Point - slope form  →  (y - y₁) = m(x - x₁)                             Two point - slope form → (y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)       Intercept form → x/a + y/b = 1                                       Normal form  →  x cos(β) + y sin(β) = L  

Given is a line passing through points (1, -1) and (5, 2).                    

The point slope form of the line is -

(y - y₁) = m(x - x₁)  

y - (- 1) = {(2 + 1)/(5 - 1)}(x - 1)

y + 1 = (3/4)(x - 1)

Therefore, the point - slope equation of line passing through points (1, -1) and (5, 2) is -

(y + 1) = (3/4)(x - 1)

To solve more questions on straight lines, visit the link below-

brainly.com/question/20400984

#SPJ2

A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 41. What is the number

Answers

To solve this problem, first we need to subtract 5 from 41, which gives us 36.  Then we divide it by 3.  The answer is 13.  We used inverse operations to solve this problem.
You have to use inverse operations to solve this. The opposite of addiction is subtraction. So 41-5=36. The opposite of multiplication is division and 36/3 is 12. The number is 12.

Triangle XYZ is reflected across the line y=x and X'= (2, -15). What are the coordinates of X,?

Answers

if reflected coordinate is (2,-15) , it mean coordinates` x and y values are changed. So, if you want to know X, reflect once again! 
Answer: (-15,2)

Answer:

the answer to this is A

Step-by-step explanation:

kasabihan sa bibliya

Answers

Ang mga Kawikaan ay hindi lamang isang antolohiya kundi isang "koleksyon ng mga koleksyon" na may kaugnayan sa isang huwaran ng buhay na tumagal ng higit sa isang sanlibong taon. Ito ay isang halimbawa ng tradisyon ng karunungan sa Biblia, at nagtataas ng mga tanong ng mga halaga, moral na pag-uugali, kahulugan ng buhay ng tao, at tamang pag-uugali.


Umaasa ako na makakatulong ito!

The next three terms in the pattern 1, 10, 19, 28, 37 are

Answers

46, 55, 64. It adds by 9 everytime.
1,10,19,28,37,?,?,?
To find the next three terms, we need to find the patterns in this sequence. In this case, we see that the first number add 9 to get the second number, the second number add 9 to get the third number, and so on. Now, we can create the formula for this which is n+9 where n is the number before the next number. Here we go:
1
1+9=10
10+9=19
19+9=28
28+9=37
37+9=46
46+9=55
55+9=64. As a result, the next three terms in the pattern 1, 10, 19, 28, 37 are 46,55,64. Hope it help!

How do you find the LCM???

I know that I asked how to find the LCM of 8 and 9 but I don't know what to multiply by to get it.

Answers

If you know the LCM then you divide it by the other number.
If you don't already know it: is 8 a factor of 9 or do they have equal factors? No.
Is 9 a factor of 8 or do they have equal factors? No.
The easy way: multiply 8 by 9 to get LCM :)

A machine factory produces 2 parts per second. One shift is 10 hours long. What is the production rate in parts per shift?

Answers

60 seconds per minute

 2 x 60 = 120 parts per minute

60 minutes per hour

120*60 = 7200 parts per hour

7200 x 10 hours = 72,000 parts per 10 hour shift

Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0

Answers

The constant variation is 1/2

Direct variation is of the form y=kx

2x-4y=0  subtract 2x from both sides

-4y=-2x  divide both sides by -4

y=x/2 or to be clear:

y=(1/2)x

So there is a constant of variation k=1/2 of the form y=kx, so this equation is a direct variation.

*note, it is called a direct variation because as the independent variable increases/decreases, the independent variable increases/decreases by the same factor...

A gift box is a rectangular prism14inches long,5inches wide,and 4inches high.If the box is to be covered in fabric ,how much fabric is needed if there is no overlap?

Answers

that's the surface area

when he length=L
width=W
and height=H


SA=2(LW+WH+LH)
so
L=14
W=5
H=4

subsitute
SA=2((14)(5)+(5)(4)+(14)(4))
SA=2(70+20+56)
SA=2(146)
SA=292

you need 292 square inches of fabric

The total fabric needed would be 292 square inches.

To calculate how much fabric is needed to cover the gift box without overlap, we must find the surface area of the rectangular prism representing the box. The formula to find the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height.

Given the dimensions of the box are 14 inches (length), 5 inches (width), and 4 inches (height), we calculate the surface area as follows:

2 (14 × 5) = 2 × 70 = 140 square inches (for the top and bottom)2 (14 × 4) = 2 × 56 = 112 square inches (for the front and back)2 (5 × 4) = 2 × 20 = 40 square inches (for the left and right sides)

The total surface area is 140 + 112 + 40 = 292 square inches of fabric needed to cover the entire box.

Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?

y = 3x + 2
6x – 2y = 10

Ryan’s answer:
I solved by adding the equations. The solution is .

y = 3x + 2 → 3x + y = 2
6x – 2y = 10 → 3x – y = 5
6x = 7
x =

6x – 2y = 10 → 6 – 2y = 10

7 – 2y = 10
–2y = –3

y = -

Jesse’s answer:
I used matrices. The solution is .



Mark’s answer:
I graphed the equations. The lines are parallel and do not intersect, so there is no solution.

Answers

6x - 2y = 10
-2y = -6x + 10...reduce by dividing by -2
y = 3x - 5....slope = 3 and y int = -5

y = 3x + 2 ...slope = 3, y int = 2

These lines are parallel. Parallel lines will have the same slope, but different y int's. There is no solution to this because ur lines never intersect.

Mark's answer is correct

6x - 2y = 10

-2y = -6x + 10

reduce by dividing by -2

y = 3x - 5

slope = 3 and y int = -5

y = 3x + 2

slope = 3, y int = 2

These lines are parallel. Parallel lines will have the same slope, but different y integers. There is no solution to this because the lines never intersect.

Mark's answer is correct

Solve the equation ax + 1 = bx for 'x'. Please be sure to include all steps.

Answers

ax + 1 = bx for x

ax + 1 = bx
ax - bx = -1
x(a-b) = -1
x = -1 /(a-b)
ax + 1 = bx
1 = bx - ax <-- Subtract ax both each side
1 = x(b - a)
1/(b - a) = x <-- Divide both sides by b - a

So, x is equal to 1/(b - a).

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road, (x2 + 3) miles downhill, and (x − 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

Answers

The answer is x= -4 if that's what they asking for

C. x²+ 2x - 4 Should be your answer to this question.

whats the property in equation 3(2x-6)=6x-18

Answers

3(2x-6)=6x-18

Distributive property

hope it helps
distributive because the 3 is distributing itself in the 2x and the -6

Plz help me with this math problem

Answers

Multiply each number bye 5

45.5 meters in 13 seconds

Answers

divide 45.5 and 13 
to get you 3.5 
i hope i helped
You would need to divide 45.5 and 13 to find how many meters in a second. The answer is 3.5.

Why would experimental probability differ from theoretical probability?

Answers

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. 


9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.

A 6
B 15.7
C 3
D 9.42

Answers

A. 6

The circumference can be found just by multiplying the diameter by pi.

So all you need to do is 18.84/3.14 which is 6.

Answer:

A. 6

Step-by-step explanation:

Write the formula c = 2πr. Substitute the value 18.84 feet for c. Solve the equation for c. Since the radius always measures one-half the length of the diameter, multiply the value of c by 2.

Sam bought 86 pounds of flour for his bakery. Every day he used the same amount of flour to make bakery items. After 10 days, Sam was left with 25.2 pounds of flour. On average, how many pounds of flour did Sam use each day?

Answers

86-25.2 = 60.8 pounds of flour used

60.8/10 = 6.08 pounds used per day

Answer:

6.08

Step-by-step explanation:

first, i subtracted 86 from 25.2 to get what he used in the 10 days, which was 60.8, then i would divide it by 10 bc of 10 days to get 6.08. Hope this helps!

Gavin agrees to buy a 6-month package deal of monthly gym passes and in turn receives a 15% discount. Write an algebraic expression to represent the total cost of the monthly passes with the discount, if x represents the cost of each monthly pass.

Answers

6*x=y
15%*y=Z
that is the equations

At the movie theatre, you pay a different price depending on your age. Children 5 and under get in for free. Children ages 6 to 18 pay $5. Everyone else pays $8. Write a piecewise function for this situation

Answers


           {  0          x ≤ 5
f(x) =  {  5           6 ≤ x < 18
           {  8          x ≥ 18

The brackets should be one big bracket.

Janet's Junk Shop is having its annual sale. Matt wants to buy a mixer that originally sold for $28.62 and is now on sale for off. Matt also has a coupon for an additional 15% off the discounted price.

How much will Matt pay for the mixer?

Answers

[tex]n\% \:\:off = (100 -n)\% \:\: of \:the\: original \:price[/tex]
[tex]FinalPrice =[/tex]
[tex](Original Price \times(\frac{100\% - Discount}{100\%}))\times(\frac{100\% - Discount_2}{100\%}) =[/tex]
[tex]\big(\$28.62\times(\frac{100\% - 25\%}{100\%})\big) \times(\frac{100\% - 15\%}{100\%}) = [/tex]
[tex]\big(\$28.62\times(\frac{3}{4})\big) \times(\frac{17}{20}) \approx \$18.25[/tex]

Matt will pay [tex]\$18.25[/tex] for the mixer

3(x+1)-[2(3-2x)-3(3-x)]

Answers

Distributive property
3x+3-2-3x+9
Combine like terms
0x+3-2+9
X=10

Write 0.8 repeating as a fraction

Answers

The answer is 8/9 i believe.

Answer: 8/9

Step-by-step explanation: I got the answer right

Sales of a new tablet grow by 10% every month. Sales for this month are at 5 thousand. Write an equation to represent this situation and then approximate the sales 6 months from now.

Answers

We start with the sale at $5,000. The growth is: p = 10% = 0.1; r = 1 + 0.1 = 1.1
The equation is:
f ( t ) = 5,000 * ( 1.1 )^t
where t it the time in months.
f ( 6 ) = 5,000 * ( 1.1 )^6 =
= 5,000 * 1.77156 = $8,857.80
Answer: The sale 6 months from now will be $8,857.80.

modal of 9
10
11
14
19
22
27
29
21
18
11
6

Answers

So, first we would have to order it from least to greatest which would be : 6,9,10,11,11,14,18,19,21,22,27,29. We would see that 11 is repeated twice . Number 11 is the modal.
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