Question

Help please ! I always award medals. Factor the quartic polynomial P(x)= 2x^4+7x^3-13x^2+7x-15. You can use the fact that x^2+1 divides P(x).

Answer 1

\[(x+5) (2 x-3) \left(x^2+1\right) \]

Answer 2

how did you get that?

Answer 3

i have access to the Mathematica program. Selected the problem expression with the mouse and clicked on the "Factor" button.

The following Mathematica expression will effect a division by x^2+1 as recommended in the problem statement:\[\text{PolynomialQuotientRemainder}\left[2 x^4+7 x^3-13 x^2+7x-15,x^2+1,x\right]= \]\[\left\{2 x^2+7 x-15,0\right\} \]The remainder is zero. So the following expression consists of at least two factors:\[\left\{2 x^2+7 x-15,x^2+1\right\} \]Turns out that the first list item can be factored, to the answer is:\[(x+5) (2 x-3)\left(x^2+1\right) \]