Question

Marya wants to factor the polynomial 36x3 – 22x2 – 144x. Which term can she add to the polynomial that would not change its greatest common factor? Check all that apply.

–11
–50xy
–40x2
24
10y

Answer 1

Given:

36x³ - 22x² - 144x

GCF:
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3

22 ÷ 2 = 11

144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3

2 is the GCF of all terms. We can add 24. It would not change the GCF of the polynomial.

36x³ - 22x² - 144x + 24

2(18x³ - 11x² - 72x + 12)

Answer 2

–50xy

–40x2

Will not change the Greatest Common Factor.

Explanation:

Greatest common factor is the highest factor that divides 2 or more number.

We can find the GCF by multiplying all the factors that are common to each number.

Factors of
`36x^(3)`=1,2,3,4,6,9,12,18, 36 and
`x`,
`x^(2)`,,
`x^(3)`

Factors of
`22x^(2)`=1,2,11,
`x` and
`x^(2)`

Factors of
`144x`=1,2,3,4,6,8,9,12,16,18,24,36 and
`x` and more.

So the common factors to all three numbers are 1,2 and x.

So GCF =
`1*2*x=2x`

If we use 11 it will change the GCF to 11.

If we use
`50xy` it will not change the GCF.

If we use 40
`40x^(2)` it will not change the GCF.

IF we use 24 it will change the GCF.

If we use 10y it will change the GCF.