Question

Complete the steps to factor the polynomial by grouping.P(x) = x3 + 5x2 – x – 5

Answer 1

P(x) = x³ + 5x² – x – 5

P(x) = x²(x+5) - (x + 5)

P(x) = (x + 5)(x² - 1)

P(x) = (x + 5) (x + 1)(x -1)

Answer 2

Answer

Find the  steps to factor the polynomial by grouping.

To prove

As given the polynomial in the question

P(x) = x³ + 5x² – x – 5

P(x) = x² (x + 5) – (x + 5)

Take  (x + 5) as common

P(x) =  (x + 5) (x² - 1)

As using the identity

(a² - b²) = (a - b)(a + b)

P(x) =  (x + 5) (x - 1)(x + 1)

Therefore the factors of the polynomial by grouping are (x + 5) and (x - 1)(x + 1) .