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

-50xy and -40x²

Explanation:

Explanation:

1) Common factor of the letters: x, x², and x³.

It is the common letter with the lowest exponent: x

2) Common factors of the coefficients (numbers): 36, 22, and 144

i) prime factors of 36: 36 = 2² × 3²

ii) prime factors of 22: 22 = 2 × 11

iii) prime factors of 144: 2⁴ × 3²

iv) Greatest common factor: the repeated number raised to the lowest power: 2.

3) Therefore, the greatest common factor of the terms 36x³ - 22x² - 144x is 2x

4) Any number that has 2x as a factor will not change this common factor.

5) Factors of the choices:

i) –11: 2x is not a factor of - 11, therefore this does not apply

ii) –50xy: 2x is a factor, since - 50xy / (2x) = - 25y, therefore this applies.

iii) –40x²: 2x is a factor, since - 40x² / (2x) = -20x, therefore this applies

iv) 24: 2x is not factor of 24, therefore this does not apply

v) 10y: 2x is not a factor of 10y, therefore this does not apply

Answer 2

-50xy and -40x²

Explanation:

1) Common factor of the letters: x, x², and x³.

It is the common letter with the lowest exponent: x

2) Common factors of the coefficients (numbers): 36, 22, and 144

i) prime factors of 36: 36 = 2² × 3²

ii) prime factors of 22: 22 = 2 × 11

iii) prime factors of 144: 2⁴ × 3²

iv) Greatest common factor: the repeated number raised to the lowest power: 2.

3) Therefore, the greatest common factor of the terms 36x³ - 22x² - 144x is 2x

4) Any number that has 2x as a factor will not change this common factor.

5) Factors of the choices:

i) –11: 2x is not a factor of - 11, therefore this does not apply

ii) –50xy: 2x is a factor, since - 50xy / (2x) = - 25y, therefore this applies.

iii) –40x²: 2x is a factor, since - 40x² / (2x) = -20x, therefore this applies

iv) 24: 2x is not factor of 24, therefore this does not apply

v) 10y: 2x is not a factor of 10y, therefore this does not apply