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

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Answer 1 · 2016-10-02T12:17:30

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

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

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

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

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

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

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

How do you factor 12x4+11x3−26x2+x+212x^4 + 11x^3 -26x^2 + x + 2?