## anonymous 5 years ago divide using synthetic division (5x^3 - 11x^2 -17x +15) / (x-3)

1. anonymous

write out the coefficients 5 -11 -17 15 3 15 12 -15 ________________ 5 4 -5 0

2. anonymous

now a word of explanation. you are dividing by x - 3. list the coefficients and put a 3 down because you are dividing by x - 3. drop the 5 3*5=15 11+15=4 3*4=12 -17+12=-5 3*-5=-15 -15+15=0 you have divided a polynomial of degree 3 by a polynomial of degree 1 which gives a polynomial of degree 2. the coefficients are 5, 4 and -5 and there is no remainder so it divides evenly. that means $\frac{5x^3-11x^2-17x+15}{x-3}=5x^2+4x-5$ or $5x^3-11x^2-17x+15=(x-3)(5x^2+4x-5)$

3. anonymous

that also means 3 is a zero of the original polynomial that is, if $f(x)=5x^3-11x^2-17x+15$ then $f(3)=0$ because $f(x)=(3-3)(5\times 3^2+4\times 3-5)=0$

4. anonymous

oops typo. i meant f(3)=0, not f(x) = 0. sorry.

5. anonymous

THANK TOY SO MUCH

6. anonymous

YOU* ..LOL

7. anonymous

welcome!