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Question
Use synthetic division to find P(3) for P(x) = x4  2x3 4x + 4.

Answer
Hi Clayton, I will be glad to help.

P(-3) will be the remainder when you synthetically divide your polynomial by x + 3.

To do synthetic division, you need all the coefficients, even the coefficient of the x^2 term which is 0 since there is no x^2 term.

         1     -2     0     -4     4
-3

Here is how synthetic division works
1) Alyways bring down the first coefficient
2) Multiply and write the product under the next coefficient
3) add and write the answer below
4) repeat steps 2 and 3 until there are no values left on top

Bringing down the leading coefficient

         1     -2     0     -4     4
-3
         1

Multiplying

         1     -2     0     -4     4
-3          -3
         1

Adding

         1     -2     0     -4     4
-3          -3
         1     -5

Continuing on gets

         1     -2     0     -4     4
-3          -3    15  -45  147
         1    -5    15  -49    151

The final term below is P(-3)
P(-3) =  151

This can be checked by plugging -3 in for x in the polynomial.

I hope this helps.

Anne

For more on synthetic division see
www.purplemath.com/modules/synthdiv.htm

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Anne Losch

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Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class

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I have a teaching certificate, I have taught Algebra 1 & 2 as well as tutored those subjects and tutored in College Algebra.

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I hold a B.S. in mathematics and computer science from an accredited university and have gone back to school to get my teacher certificate. I hold more than enough credits for an education minor.

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