Question

USING FACTOR THEOREM , VERIFY WHETHER G ( x ) IS A FACTOR OF P(x)
1 ) P ( x ) = x^4 - 4x^2 + 2x + 1 ,
Q ( x) = x - 1

Answer 1

P(x) = x⁴ - 4x² + 2x + 1

G(x) = x-1

Zero of G(x) = 1

Therefore,

p(1) = (1)⁴ - 4(1)² + 2(1) + 1

= 1 - 4 + 2 + 1

= 4 - 4

= 0

Since the remainder here comes zero

Therefore, G(x) is a factor of p(x) by factor theorem.