Question

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x³ - 3x² + 4x - 4 and g(x) = x - 2

Answer 1

p(x) = x³ - 3x² + 4x - 4 and g(x) = x - 2
To check whether x - 2 is a factor of p(x) now put x = 2 in equation (i), we get
p(2) = (2)³ - 3(2)² + 4(2) -4
= 8 - 3 x 4 + 8 - 4
= 8 - 12 + 8 - 4
= 16 - 16 = 0
Since, p(2) = 0, so by factor theorem (x - 2) is a factor of p(x).