SOLUTION: Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown: <pre> -1|-2 -5 4 2 3 |___________ -2 -3 7</pre> What is the value of f(-1)?

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Question 1037649: Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown: 
-1|-2 -5 4 2 3 
  |___________ 
   -2 -3 7

What is the value of f(-1)?

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

-1|-2 -5 4 2 3 
  |___________ 
   -2 -3 7

That's not complete.  It should be

-1|-2 -5  4  2 3 
  |    2  3 -7 5 
   -2 -3  7 -5 8

Synthetic division is a shortcut for long division
of a polynomial by a binomial of the form x±A:

        -2x³-3x²+7x-5+
x+1)-2x4-5x³+4x²+2x+3
    -2x4-2x³
        -3x³+4x²
        -3x³-3x²
             7x²+2x
             7x²+7x
                -5x+3
                -5x-5
                    8       

The remainder when you divide a polynomial by x+1 is always 
the same as what you get if you substitute (-1) in the polynomial.

-2(-1)4-5(-1)³+4(-1)²+2(-1)+3
-2(1)-5(-1)+4(1)-2+3
-2+5+4-2+3
   8

Notice that the 8 remainder when you divide by x+1 
using long division or the opposite sign -1 with
synthetic division is the same answer as if you
had substituted -1 into the polynomial.  So f(-1)=8

Edwin
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