Question

Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?

Answer 1

`x^3 - 7x^2 - 5x + 35=(x-7)(x-√(5))(x+√(5))`

Explanation:

We are given a expression:

`x^3 - 7x^2 - 5x + 35`

`x^3 - 7x^2 - 5x + 35\\\\=x^2(x-7)-5(x-7)\\\\=(x^2-5)(x-7)`

We know that
`a^2-b^2=(a-b)(a+b)`

So,
`x^2-5=x^2-(√(5))^2 \\\\=(x-√(5))(x+√(5))`

So,
`x^3 - 7x^2 - 5x + 35=(x-7)(x-√(5))(x+√(5))`

Answer 2

`(x-7)(x-√(5))(x+√(5))`

Explanation:

The given expression is

`x^3-7x^2-5x+35`

Factor the first two and the last two.

`x^2(x-7)-5(x-7)`

`(x-7)(x^2-5)`

Apply difference of two squares to the leftmost factor.

`(x-7)(x-√(5))(x+√(5))`