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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 :

W0lf93

The polynomial expression is P(x)=36x3 – 22x2 – 144x,
it can be written P(x)=36x².x – 22x.x – 144.x, each term is factor of x. We can affirm that x is the greater factor, because P(x) is can be expressed as P(x)= x (36x² – 22x – 144). So if we add this last by –50xy, the common factor doesn’t change. That is P(x)- 50x.y= x (36x² – 22x – 144)–50 xy = x.(36x² – 22x – 144 - 50 y). the true answe is B –50xy.

answer : \(-50xy\ and\ -40x^2\)

We find greatest common factor for the given polynomial

The prime factors of \(36x^3 = 3 * 2 * 3* 2 * x *x *x\)

The prime factors of \(-22x^2 = -2 * 11 * x* x\)

The prime factors of \(-144x = -2 * 3 * 2 * 2 * 3 * 2 * x\)

the greatest common factor of the terms 36x³ - 22x² - 144x is 2x

Now we check the options that has common factor 2x

–11
= -11

–50xy  = - 2 5 5 x y that has factor 2x

–40x^2  = -2 2 5 2 x x that has factor 2x

24  = 3 2 6

10y= 5 2 * y

\(-50xy\ and\ -40x^2\) she can add to the polynomial that would not change its greatest common factor 2x.

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