How do you factor $12x^4 + 11x^3 -26x^2 + x + 2$ ?

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Answer 1 · 2016-10-02T12:17:30

$(x+2)(12x^3-13x^2+1)$

There are 5 terms, so we will have to group them first.
The first 3 terms have an obvious factor of $x^2$
Let's try with those...

$color(red)((12x^4 + 11x^3 -26x^2)) + (x + 2)$

$=color(red)(x^2)(12x^2+11x-26) + (x+2)$

$=x^2(12x-13)color(blue)((x+2)) + color(blue)((x+2))$

$=color(blue)((x+2))(x^2(12x-13) +1)$

$=(x+2)(12x^3-13x^2+1)$

How do you factor 12x^4 + 11x^3 -26x^2 + x + 212x^4 + 11x^3 -26x^2 + x + 2?