Problema Solution
Use the remainder theorem to find the remainder when f(x) is divided by x+5. Then use the factor theorem to determine whetherx +5 is a factor of f(x). Please show all of your work.
f(x)=x^4+5x^3-7x^2-32x+15
Answer provided by our tutors
f(-5) = (-5)^4+5(-5)^3-7(-5)^2-32(-5)+15
= 625 -625 -175 +160+15
= 0 - 175 + 175
= 0 - 0 = 0
0 is the remainder when f(x) is divided by x+5
Therefore, by factor theorem, x+5 is a factor of f(x).