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

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.

Answer 2

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.