Question: Given that x^{2}+2x-3 is a factor f(x)=x^{4}+2x^{3}-7x^{2}+ax+b, find a and b and hence factor f(x) completely.

Hi Maha,

x^{2 }+ 2x - 3 = (x + 3)(x - 1) and hence, since x^{2 }+ 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