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

1. anonymous

2. zepdrix

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: $$\large\rm (x-1)$$

3. zepdrix

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

4. anonymous

5 or 3 ?

5. zepdrix

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

6. zepdrix

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

7. anonymous

Thank you !

8. zepdrix

yay team \c:/