Question

Solve by factoring: X^3+7x^2-x-7=0

Answer 1

`{x}^(3) + 7 {x}^(2) - x - 7 = 0 \\ \Leftrightarrow {x}^(2) (x + 7) - (x + 7) = 0 \\ \Leftrightarrow ( {x}^(2) - 1)(x + 7) = 0 \\ \Leftrightarrow (x - 1)(x + 1)(x + 7) = 0 \\ \Leftrightarrow x = - 7 \: \vee \: x = - 1 \: \vee \: x = 1`

Answer 2

`\boxed{\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}}`

Explanation:

Factor
`\bold{x^3+7x^2-x-7}`

`\bold{\left(x+7\right)\left(x^2-1\right)}`

Factor
`\bold{0}`

`\bold{0}`

Rewrite Equation

`\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}`