Question

When f(x) is divided by x + 4, the quotient is x2+5x−3+2x+4. What is f(−4)?

Answer 1

f(-4)=0

Explanation:

when f(x) is divided by (x+4) you get (x²+5x-3+2x+4), so:

f(x)=(x+4)*(x²+5x-3+2x+4)

f(x)=(x+4)*(x²+7x-1)

f(x)=x(x²+7x-1)+4(x²+7x-1)

f(x)=x³+7x²-x+4x²+28x-4

f(x)=x³+11x²+27x-4

Now we know f(x), sub in -4 for x to get f(-4):

f(x)=x³+11x²+27x-4

f(-4)=(-4)³+11(-4)²+27(-4)-4

f(-4)=-64+11(16)-108-4

f(-4)=-64+176-112=0

f(-4)=0