Question

Factorise x3+x2-4x-4

Answer 1

Hello!

Answer:

`\Large \boxed{\sf (x-2)(x+2)(x+1)}`

Explanation:

→ We want to factorize this expression:

`\sf x^3+x^2-4x-4`

◼ Factorize by grouping:

`\sf x^3+x^2-4x-4 \\\\=x^3+x^2+2x - 6x-4\\\\= x(x^2 + 3x + 2) - 2(x^2 + 3x + 2)\\\\= (x-2)(x^2 + 3x + 2)\\\\= (x-2)(x^2 + x + 2x + 2)\\\\= (x-2)(x(x+1) + 2(x+1))\\\\ \boxed{\sf= (x-2)(x+2)(x+1)}`

Conclusion:

The expression x³ + x² - 4x - 4 is equal to (x - 2)(x + 2)(x + 1).