4x2 - 14x + 6

x3 - 7x2 + 12x

What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common

factors.

Answer is given below.

Step-by-step explanation:

let us solve the numerator first

=4x²-14x+6

=2 (2x²) + 2 (-7x) + 2 (3)

= GCF of the terms of the numerator is 2.

denominator

x³-7x²+12x

x (x²) + x (-7x) + x (12)

GCF of the terms of the denominator is x.

factorise the numerator

4x²-14x+6

4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no. s are added they should give - 14)

(4x²-2x) + (-12x+6)

2x (2x-1) - 6 (2x-1)

(2x-6) (2x-1)

factors are

(2x-6), (2x-1)

denominator

this can also be done by splitting the middle term

x³-7x²+12x

x³-3x²-4x²+12x

(x³-3x²) + (-4x²+12x)

x² (x-3) - 4x (x-3)

(x²-4x) (x-3)

factors are

(x²-4x), (x-3)