How do you use synthetic substitution to find p(-3) for p(x)=4x3−5x2+7x−10?

1 Answer
Pythagoras
Sep 20, 2015

-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.

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