Given 5x3+8x2−7x−6. 1) the binomial (x+2) is a factor of the polynomial expression. describe how you know it is a factor. 2) the binomial (x+1) is not a factor of the polynomial expression. explain how you know it is not a factor.

ANSWER TO QUESTION 1

Given

We can use the factor theorem to determine if

is a factor of the polynomial or not.

According to this theorem, if is a factor of , then .

How did we get the ?

We set and then solve to obtain .

So now let us plug in in to the function to see if it will simplify to zero.

Since the result simplifies to zero, we conclude that

is a factor of

ANSWER TO QUESTION 2

We have the function,

We can use the remainder theorem to show that

is NOT a factor of the polynomial.

According to this theorem, if is not a factor of , then .

So now let us plug in in to the function to see if it will simplify to non-zero number.

Since the result simplifies to a non zero number, we conclude that

is NOT a factor of