Question

Write the expression as a product of binomials using the Distributive Law.

a) 2x²−16x−15
b) 2x²−14x−15
c) 2x² −15x−14
d) 2x² −15x−16

Answer 1

To write the expression as a product of binomials, we need to factor the quadratic expression. Some expressions can be factored, while others cannot.

Step-by-step explanation:

To write the expression as a product of binomials using the Distributive Law, we need to factor the quadratic expression. Let's consider each option:

a) 2x² - 16x - 15

To factor this expression, we need to find two numbers whose product is -15 and whose sum is -16. The numbers -5 and 3 satisfy these conditions.

Therefore, we can rewrite the expression as (2x + 3)(x - 5).

b) 2x² - 14x - 15

This expression cannot be factored, as there are no two numbers whose product is -15 and whose sum is -14.

c) 2x² - 15x - 14

To factor this expression, we need to find two numbers whose product is -28 and whose sum is -15. The numbers -4 and 7 satisfy these conditions.

Therefore, we can rewrite the expression as (2x + 7)(x - 2).

d) 2x² - 15x - 16

This expression cannot be factored, as there are no two numbers whose product is -16 and whose sum is -15.

So, the only expressions that can be written as a product of binomials are a) and c).