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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

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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