Question

42. The area of a rectangle is 12x³- 18x² + 6x. The width is equal to the GCF What could the dimensions of the rectangle be? A. 6x(2x² – 3x) B. 3(4x³ - 6x² + 2x) C. x(12x²- 18x + 6) D. 6x(2x² - 3x + 1)​

Answer 1

D. 6x(2x² - 6x + 1)

GCF - Greatest Common Factor

It is simply the largest of the common factors.

We have:

12x³- 18x² + 6x

We find GCF of 12, 18 and 6:

GCF(12, 18, 6) = 6

12 = 2 · 6

18 = 3 · 6

6 = 1 · 6

and GCF of x³, x² and x:

GCF(x³, x², x) = x

x³ = x² · x

x² = x · x

x = 1 · x

Therefore:

12x³- 18x² + 6x = 6x(2x² - 6x + 1)