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

The factored form of the polynomial expression will be  (x+1)(x-1)(x+5)

Given the polynomial function expressed as

We are to factor the polynomial by grouping. On grouping, we have:

P(x) = (x³+5x²)-(x+5)

P(x) = x²(x+5)-1(x+5)

P(x) = (x²-1)(x+5)

According to the difference of two squares, a²-b² = (a+b)(a--b)

The polynomial function will become

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

Hence the factored form of the polynomial expression will be  (x+1)(x-1)(x+5)

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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) .

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