Respuesta :
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) .
The factored form of the polynomial expression will be (x+1)(x-1)(x+5)
Given the polynomial function expressed as [tex]P(x) = x^3 + 5x^2 - x -5[/tex]
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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