Question

which expression is equivalent to the polynomial given below? 54x + 30
a. 6(9x + 5)
b. 6(9x + 4)
c. 9(5x + 5)
d. 6(9x + 30)

Explanation:

Step1: Factor out the GCF

Find the greatest - common factor of 54 and 30. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The GCF of 54 and 30 is 6.

Step2: Rewrite the polynomial

We can rewrite 54x + 30 as 6\times9x+6\times5. Then, by the distributive property a(b + c)=ab+ac, we can factor out the 6 to get 6(9x + 5).

Answer:

A. 6(9x + 5)