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. a. 11 b. 50xy c. 40x2 d. 24 e. 10y

Answer 1

`50xy` and
`40x^2`.

Explanation:

The given polynomial is
`36x^3-22x^2-144x`.

The prime factorization of each term are;

`36x^2=2^2* 3^2* x^3`

`-22x^2=-2* 11* x^2`

`-144x=-2^4* 3^2* x`

The greatest common factor of these three terms is
`2x`.

Now observe that:

The GCF of
`2x` and 11 is 1

The GCF of
`2x` and 50xy is 2x

The GCF of
`2x` and
`40x^2` is 2x

The GCF of
`2x` and 24 is 2

The GCF of
`2x` and 10y is 2

The correct options are
`50xy` and
`40x^2`.