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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

Verified Answer :

meerkat18

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)

Limosa

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.



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