Question

Use the remainder theorem to show that (x+1) is a factor off(x) = 2x3 – 7x2 – 5x + 4For full credit please answer both parts A and B. (each part is worth 2 points)A. In the answer blank show your work.B. Explain why your work proves that (x+1) is a factor.

Answer 1

we have

f(x) = 2x^3 – 7x^2 – 5x + 4

If (X+1) is a factor

then

f(x)/(x+1)=q(x)

f(x)=(x+1)q(x)+r(x)

The remainder theorem tells us that for any polynomial f(x) , if you divide it by the binomial x−a , the remainder is equal to the value of f(a)

so

For x=-1

f(-1)=2(-1^3)-7(-1^2)-5(-1)+4

f(-1)=-2-7+5+4

f(-1)=0

that means

the remainder is zero --------> that prove (x+1) is a factor