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

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
4) repeat steps 2 and 3 until there are no values left on top

1     -2     0     -4     4
-3
1

Multiplying

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

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

Algebra

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Anne Losch

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