# How to fully factor a polynomial of 4th degree?

How to fully factor this polynomial? $$2x^4+3x^3-32x^2-48x$$

Can anyone describe the full steps to factor it? Thanks for the help.

• There is a general formula for a 4th order polynomial, but it is way too long to remember. Just try to guesstimate two solutions and then quadratic formula the rest. I'm sorry I can't be more specific. – Simon Means Dec 13 '14 at 22:38
• haha +1 for guesstimate:D – Marc Dec 13 '14 at 22:41
• As Edward has shown, there is not need for the quartic formula or guestimation. Cubic polynomials $ax^3+bx^2+cx+d$ (which this becomes when an $x$ is factored out) are easily factorable when $a/c=b/d$ or $a/b=c/d$. – Mike Earnest Dec 13 '14 at 23:20

$$2x^4+3x^3-32x^2-48x$$ $$=x(2x^3+3x^2-32x-48)$$ $$=x(x^2(2x+3)-16(2x+3))$$ $$=x(2x+3)(x^2-16)$$ $$=x(2x+3)(x-4)(x+4)$$