How do you use synthetic substitution to find p(-3) for #p(x)=4x^3-5x^2+7x-10#?

1 Answer
Sep 20, 2015

Answer:

-184

Explanation:

Well, you need to know what a synthetic substitution is. I am not going to explain this here but just show you the steps.
I didn't know what it was until I read this question so I googled it and found some great Youtube videos that explain how to do the trick. Here is one, for example

So in this question, we want to find p(-3) so write down #-3# on the left, and the coefficients of the polynomial #4, -5, 7, -10#.

Here are the steps:
- drop down the 4.
- multiply 4 by -3. #4*-3=-12#
- write -12 below the -5.
- add -5 and -12. #-5+(-12)=-17#
- multiply -17 by -3. #-17*-3 = 51#
- write 51 below the 7.
- add 51 and 7. #7+51=58#
- multiply 58 by -3. #58*-3=-174#
- write -174 below the -10.
- add -174 and -10. #-10+(-174)=-184#

i.e. #p(-3)=-184#

You can check if this answer is correct by directly substituting in the original equation:

#4*(-3)^3= 4*9*-3 = 36*-3=-108#
#-5*(-3)^2=-5*9=-45#
#7*(-3)=-21#
#-10=-10#
i.e. #p(-3)=-108-45-21-10=-184#

That's it. Hope it helped.