Complete the steps to factor the…

Maths Questions

Complete the steps to factor the polynomial by grouping. Given P(x) = x¬≥ + 5x¬≤ – x – 5, how do you factor it into the form P(x) = (x¬≤ – )(x + 5) and ultimately into P(x) = (x – )(x + 1)(x + )?

Answer

[tex]p(x)=(x+5)(x-1)(x+1)[/tex]Step-by-step explanation: We start with the polynomial [tex]p(x)=x^3+5x^2-x-5[/tex]. First, we group the terms into two pairs: [tex]p(x)=(x^3+5x^2)-x-5[/tex]. Next, we can factor out -1 from the second pair: [tex]p(x)=(x^3+5x^2)-1times (x+5)[/tex]. In the first pair, we can observe that we can factor out x^2: [tex]p(x)=x^2(x+5)-1times (x+5)[/tex]. Now, noticing that (x+5) is common, we factor it out: [tex]p(x)=(x+5)(x^2-1)[/tex]. Finally, we factor x^2-1 as a difference of squares: [tex]p(x)=(x+5)(x-1)(x+1)[/tex].

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