Question

Using long division method show that the polynomial p(x) = x^3 + 1 is divisible by q(x) = x + 1.Verify your using factor theorem.

Answer 1

Answer:

Long division. x^2 - x + 1. ____________ x+1 [ x^3 + 1. [ x^3 + x^2. ---------------- -x^2 + 1. x² - x + 1. Using factor theorm: a³ + b³ = (a + b)(a² – ab + b²) So, x³ + 1 = x³ + 1³ = (x+1)(x² - 2x + 1) and (x³ + 1) / (x+ 1) = (x+1)(x² - 2x + 1) / (x + 1) The (x + 1) brackets cancel out and we are left with. x² - 2x + ...