Question

What is x^2+10x+25 ——————- x^2-2x-35 in simplest form? State any restrictions on the variable. The simplified form is _______.

Answer 1

We are to simplify:

x^2+10x+25

x^2-2x-35

Lets factor x² + 10x + 25: (x + 5)²

= (x + 5)²

x² -2x-35

Let's factor x² - 2x - 35: (x + 5)(x - 7)

= (x + 5)²

(x + 5)(x - 7)

= Apply exponent rule: a^b+c = a^b . a^c

(x + 5)² = (x + 5)(x + 5)

= (x + 5)(x + 5)

(x + 5)(x - 7)

cancel out common factor: x + 5

= x + 5

x - 7