What is the factorization of the polynomial graphed below? Assume it has no constant factor.

Question

anonymous · Answer

attachment

zepdrix · Answer

This polynomial has three distinct roots, and the shape of an odd function.
So we should expect a third degree polynomial.

One of the roots of this polynomial is $\large\rm x=1$.
See how it passes through x=1? :)

Subtract 1 from each side,$$\large\rm x-1=0$$That tells us that one of the factors of our polynomial will be: $\large\rm (x-1)$

zepdrix · Answer

How bout the other roots?
See any others? :)

anonymous · Answer

5 or 3 ?

zepdrix · Answer

Mmm 3 sounds good: $\large\rm x=3\qquad\to\qquad (x-3)=0$
5 also: $\large\rm x=5\qquad\to\qquad (x-5)=0$

zepdrix · Answer

So bam! There's your polynomial! :)
Just multiply those factors together.
$\large\rm =(x-1)(x-3)(x-5)$

anonymous · Answer

Thank you !

zepdrix · Answer

yay team \c:/