SOLUTION: Factor 15x3 - 5x2 + 6x - 2 by grouping. What is the resulting expression? (5x2 + 2)(3x - 1) (5x2 - 2)(3x + 1) (15x2 + 2)(x - 1) (15x2 - 2)(x + 1)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Factor 15x3 - 5x2 + 6x - 2 by grouping. What is the resulting expression? (5x2 + 2)(3x - 1) (5x2 - 2)(3x + 1) (15x2 + 2)(x - 1) (15x2 - 2)(x + 1)      Log On


   

Question 1209791: Factor 15x3 - 5x2 + 6x - 2 by grouping. What is the resulting expression?
(5x2 + 2)(3x - 1)
(5x2 - 2)(3x + 1)
(15x2 + 2)(x - 1)
(15x2 - 2)(x + 1)
Found 2 solutions by math_tutor2020, Edwin McCravy:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

15x%5E3+-+5x%5E2+%2B+6x+-+2

= %2815x%5E3+-+5x%5E2%29+%2B+%286x+-+2%29 pairing terms into two groups

= 5x%5E2%283x+-+1%29+%2B+2%283x+-+1%29 factor each group separately

= %285x%5E2%2B2%29%283x+-+1%29 pull out the GCF 3x-1

Therefore,
15x%5E3+-+5x%5E2+%2B+6x+-+2=%285x%5E2%2B2%29%283x+-+1%29
is an identity. This is a true equation for any x value you plug in.
Verification using WolframAlpha (there are other similar online calculators)
Alternatively you can FOIL out the expression (5x^2+2)(3x-1) to arrive back at 15x^3 - 5x^2 + 6x - 2


Answer: Choice A

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Factor 5x2 out of the first two terms:

5x2(3x - 1) + 6x - 2

Factor +2 out of the last two terms:

5x2(3x - 1) + 2(3x - 1)

Factor (3x - 1) out of the two terms:

(3x - 1)(5x2 + 2)

That's the same as

(5x2 + 2)(3x  -  1)

the first choice.

Edwin