Question

Factor the following quadratic expression: x^2 + 7x - 30. Write the steps. a) (x - 5)(x + 6) b) (x + 5)(x - 6) c) (x - 3)(x + 10) d) (x + 3)(x - 10)

Answer 1

Explanation:

To factor any quadratic equation in
`x^(2)` + bx + c form,

Step 1: Find factors of c that add up to b.

This means we will need to find two numbers that will multiply to be equal the constant term c, and will also add up to b, the coefficient on the linear x-term in the middle. In this case c is -30 and b is 7. The two numbers will be 10 and -3 since 10 (-3) = -30 and 10 + (-3) = 7. Let's name these factors as p and q.

Step 2: Factor the quadratic equation as (x + p)(x + q).

(x - 3) (x + 10)

Answer: c.