Factor.

Question

A.) 16y - 56   B). -2x-8   C). 5a - 15b + 25

Answer 1

(A) The expression is 16y - 56.

First find the GCF of 16y and 56.

Factor the each monomial and Circle the common prime factors.

The product of the common prime factors, 2 · 2 · 2 or 8, is called the greatest common factor of 16y and 56.

Write each term as the product of the GCF and its remaining factors.Then use the Distributive Property to factor out the GCF.

16y - 56 = 8(2 · y) - 8(7)

             = 8(2y) - 8(7)

             = 8(2y - 7).

The completely factored form of 16y - 56 is 8(2y - 7).

(B) The expression is -2x - 8.

First find the GCF of 2x and 8.

Factor the each monomial and Circle the common prime factors.

The product of the common prime factors, 2 is the greatest common factor of 2x and 8.

Write each term as the product of the GCF and its remaining factors.Then use the Distributive Property to factor out the GCF.

-2x - 8 = -2(x) - 2(2 · 2)

             = -2(x) - 2(4)

             = -2(x + 4).

The completely factored form of -2x - 8 is -2(x + 4).

(C) The expression is 5a - 15b + 25.

First find the 5a, 15b and 25.

Factor the each monomial and Circle the common prime factors.

GCF : 5.

Write each term as the product of the GCF and its remaining factors.Then use the Distributive Property to factor out the GCF.

5a - 15b + 25 = 5(a) - 5(3 · b) + 5(5)

                      = 5(a) - 5(3b) + 5(5)

                      = 5(a - 3b + 5).

The completely factored form of 5a - 15b + 25 is 5(a - 3b + 5).