Question

${14n}^{3} - {35n}^{2} + 28$Simplify the following problem

Answer 1

Simplify

$14n^3-35n^2+28$

First, we take 7 as a common factor of all terms:

$14n^3-35n^2+28=7(2n^3-5n^2+4)$

Now we need to factor the expression in parentheses. There is no direct method to do it, just by guessing or trial and error to find the 'hidden' factor.

$2n^3-5n^2+4=2n^3-4n^2-n^2+2n-2n+4$

The transformations above will help us to find a common factor. We'll factor in pairs:

$2n^3-4n^2-n^2+2n-2n+4=2n^2(n-2)-n(n-2)-2(n-2)$

Factoring n-2:

$2n^3-4n^2-n^2+2n-2n+4=(n-2)(2n^2-n-2)$

Thus, the final simplification is:

$14n^3-35n^2+28=7(n-2)(2n^2-n-2)$