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

Question

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

anonymous · Answer

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

anonymous · Answer

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 
$$5x^3-11x^2-17x+15=(x-3)(5x^2+4x-5)$$

anonymous · Answer

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 
$$f(x)=(3-3)(5\times 3^2+4\times 3-5)=0$$

anonymous · Answer

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

anonymous · Answer

THANK TOY SO MUCH

anonymous · Answer

YOU* ..LOL

anonymous · Answer

welcome!