Question

The area of a rectangle is x 2 – 3x – 28. If the width is (x – 7), what is the length? (hint: it is a binomial)

Answer 1

(x + 4)

Explanation:

By factoring the area expression we obtain the length, that is

x² - 3x - 28

Consider the factors of the constant term (- 28) which sum to give the coefficient of the x- term (- 3)

The factors are - 7 and + 4 , since

- 7 × 4 = - 28 and - 7 + 4 = - 3 , then

x² - 3x - 28 = (x - 7)(x + 4)

with width (x - 7) and length (x + 4)