Question

Complete the steps to factor the polynomial by grouping. P(x) = x3 + 5x2 – x – 5 P(x) = x2 (x + ) – (x + 5) P(x) = (x2 – )(x + 5) P(x) = (x – )(x + 1)(x + )

Answer 1

P(x)=x^2(x+5)-(x+5)

P(x)=(x^2-1) (x+5)

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

Explanation:

Answer 2

`p(x)=(x+5)(x-1)(x+1)`

Explanation:

we are given polynomial as

`p(x)=x^3+5x^2-x-5`

We can group first two terms and last two terms

`p(x)=(x^3+5x^2)-x-5`

We can factor out -1 from last two terms

`p(x)=(x^3+5x^2)-1* (x+5)`

We can see that x^2 is common in first two terms

so, we can factor out x^2 from first two terms

`p(x)=x^2(x+5)-1* (x+5)`

we can see x+5 is in both terms

so, we can factor out x+5

`p(x)=(x+5)(x^2-1)`

we can also factor it as

`p(x)=(x+5)(x-1)(x+1)`