Question

Marya wants to factor the polynomial 36x^3 – 22x^2 – 144x. Which term can she add to the polynomial that would not change its greatest common factor? Check all that apply.

Answer 1

Answer:

-50xy

-40x²

Step-by-step explanation:

1. The greatest common of the variable is the variable with the lowest exponent, as you can see, the exponents are: 3,2 and 1. The lowest exponent is 1, then, it is x.

2. The greatest common factor of the coefficients is 2,  because all of them are divisible by 2.

3. Therefore, you can add a term that has the greatest common factor 2x. This means that the term must have the variable "x" and the coefficient must be divisible by 2:

4. The terms -50xy and -40x² has the greatest  common factor 2x.

Answer 2

Answer:

-50xy and -40x²

Step-by-step explanation:

To find the term which would not change its greatest common factor when added to the given polynomial, we need to find the common factors for the variables and its coefficients.

Common factors of the variables are x, x²and x³; and

the common variable with the lowest exponent is x.

Common factors of the coefficients of x are 36, 22, and 144

We further need to look for prime factors for each of these coefficients:

prime factors of 36 = 2² × 3²

prime factors of 22 = 2 × 11

prime factors of 144 = 2⁴ × 3²

Greatest common factor which is the repeated number raised to the lowest power = 2.

So the greatest common factor for the given polynomial would be 2x.

Now check for the factors for the given options:

–11: 2x is not a factor of - 11, so it is not a correct option.

–50xy: 2x is a factor, since - 50xy / 2x = - 25y, therefore it is correct.

–40x²: 2x is a factor, since - 40x² / (2x) = -20x, therefore it is correct.

24: 2x is not factor of 24, so it is not a correct option.

10y: 2x is not a factor of 10y, so it is also not a correct option.