How do you factor by grouping $t^3+2t^2-7t-14$ ?

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Answer 1 · 2015-05-10T11:50:01

$t^3 + 2t^2 - 7t - 14 = (t^3 + 2t^2) - (7t + 14)$
$= t^2(t + 2) - 7(t + 2) = (t^2 - 7)(t + 2)$

So grouping the first two terms together and the last two terms together allows us to notice the common factor $(t + 2)$ .

If we allow irrational coefficients, $(t^2 - 7)$ factors as $(t - sqrt(7))(t + sqrt(7))$ .

How do you factor by grouping t^3+2t^2-7t-14t^3+2t^2-7t-14?