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

Answer:

–50xy

–40x2

Will not change the Greatest Common Factor.

Step-by-step 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 = $1\times2\timesx=2x$

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.

Answer 2

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)