Question

X^3+7x^2-5x-35 factor completely

Answer 1

`\huge\boxed{x^3+7x^2-5x-35=(x+7)(x-\sqrt5)(x+\sqrt5)}`

Explanation:

`x^3+7x^2-5x-35=x^2(x+7)-5(x+7)=(x+7)(x^2-5)\\\\=(x+7)(x^2-(\sqrt5)^2)=(x+7)(x-\sqrt5)(x+\sqrt5)\\\\\text{Used:}\\\\\text{the distributive property:}\ a(b+c)=ab+ac\\\\a^2-b^2=(a-b)(a+b)\\\\(√(a))^2=a,\ \text{for}\ a\geq0`