Given
color(white)("XXX")x^3+x^2-16x-16=0XXXx3+x2−16x−16=0
By observation we can see that x=-1x=−1 is an obvious solution.
That is (x+1)(x+1) is a factor of the left side of the given equation.
Using polynomial long division or synthetic division we get:
color(white)("XXX")(x+1)(x^2-16)=0XXX(x+1)(x2−16)=0
(x^2-16)(x2−16) is obviously the difference of squares with
color(white)("XXX")(x^2-16)=(x+4)(x-4)XXX(x2−16)=(x+4)(x−4)
So we have
color(white)("XXX")(x+1)(x+4)(x-4)=0XXX(x+1)(x+4)(x−4)=0
which implies
(x+1)=0color(white)("xxx")rarrcolor(white)("xxx")x=-1(x+1)=0xxx→xxxx=−1
or
(x+4)=0color(white)("xxx")rarrcolor(white)("xxx")x=-4(x+4)=0xxx→xxxx=−4
or
(x-4)=0color(white)("xxx")rarrcolor(white)("xxx")x=4(x−4)=0xxx→xxxx=4
