Question

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

Answer 1

Answer:

$(x-7)(x-\sqrt{5})(x+\sqrt{5})$

Step-by-step 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.

$(x-7)(x-\sqrt{5})(x+\sqrt{5})$

Answer 2

Answer:

$x^3 - 7x^2 - 5x + 35=(x-7)(x-\sqrt{5})(x+\sqrt{5})$

Step-by-step 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, $x^2-5=x^2-(\sqrt{5})^2 \\\\=(x-\sqrt{5})(x+\sqrt{5})$

So, $x^3 - 7x^2 - 5x + 35=(x-7)(x-\sqrt{5})(x+\sqrt{5})$