Question

) By using factor theorem in the following examples, determine whether q(x) is a factor p(x) or not. (1) p(x) = x3 - x2 - x - 1, q(x) = x - 1 .​

Answer 1

Step-by-step explanation:

p(x) = x3 – x2 – x – 1 Divisor = q(x) = x – 1 ∴ take x = 1 Remainder = p(1) p(x) = x3 – x2 – x – 1 ∴ P(1) = (1)3 – (1)2 – 1 – 1 = 1 – 1 – 1 – 1 = -2 ≠ 0 ∴ By factor theorem, x – 1 is not a factor of x3 – x2 – x – 1. ii. p(x) = 2x3 – x – 45 Divisor = q(x) = x – 3 take x = 3 Remainder = p(3) p(x) = 2x3 – x2 – 45 P(3) = 2(3)3 – (3)2 – 45 = 2(27) – 9 – 45 = 54 – 9 – 45 = 0 ∴ By factor theorem, x – 3 is a factor of 2x3 – x2 – 45.