Question

Without actual division, prove that x4 +2x3 -2x2 +2x-3 is exactly divisible by x2 +2x -3.

Answer 1

Step-by-step explanation:

f(x)=x⁴+2x³-2x²+2x-3.

g(x)=x²+2x-3

g(x)=(x+3)(x-1)

g(x)=3 and g(x)=1

If x²+2x-3 is a factor then f(3) and f(1) is zero