x^2+2x-3 is a factor f(x)=x^4+2x^3-7x^2+ax+b

Name: Maha
Who is asking: Student
Level of the question: Secondary

Question: Given that x²+2x-3 is a factor f(x)=x⁴+2x³-7x²+ax+b, find a and b and hence factor f(x) completely.

Hi Maha,

x²+ 2x - 3 = (x + 3)(x - 1) and hence, since x²+ 2x - 3 divides f(x), -3 and 1 are roots of f(x). Thus

f(-3) = f(1) = 0

This allows you to solve for a and b.

Penny