Question

for question 4-5, factor the given polynomials.

1. $21x^{3}-12x^{2}+14x - 8$

a)
b)
c)
d)

1. $9x^{2}-25$

a)
b)
c)
d)

Explanation:

Step1: Group polynomial 4 terms

$21x^3 - 12x^2 + 14x - 8 = (21x^3 - 12x^2) + (14x - 8)$

Step2: Factor out GCF from groups

$= 3x^2(7x - 4) + 2(7x - 4)$

Step3: Factor out common binomial

$=(3x^2 + 2)(7x - 4)$

Step4: Recognize polynomial 5 as difference of squares

$9x^2 - 25 = (3x)^2 - 5^2$

Step5: Apply difference of squares rule

$=(3x + 5)(3x - 5)$

Answer:

1. $\boldsymbol{(3x^2 + 2)(7x - 4)}$
2. $\boldsymbol{(3x + 5)(3x - 5)}$