How do you factor the expression $14x^3 - 21x^2 - 2x + 3$ ?

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Answer 1 · 2015-12-29T00:12:40

Factor by grouping then using the difference of squares identity to find:

$14x^3-21x^2-2x+3$

$=(7x^2-1)(2x-3)$

$=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)$

The difference of squares identity can be written:

$a^2-b^2 = (a-b)(a+b)$

Use this with $a=sqrt(7)x$ and $b=1$ to find:

$14x^3-21x^2-2x+3$

$=(14x^3-21x^2)-(2x-3)$

$=7x^2(2x-3)-1(2x-3)$

$=(7x^2-1)(2x-3)$

$=((sqrt(7)x)^2-1^2)(2x-3)$

$=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)$

How do you factor the expression 14x^3 - 21x^2 - 2x + 314x^3 - 21x^2 - 2x + 3?