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Algebra II: Polynomials

Problems

Synthetic Division

The Rational Zeros Theorem

Problem : What is 3x 5 -7x 4 -11x 3 +31x 2 - 28x - 60 divided by x - 3 ?

3x 4 +2x 3 -5x 2 + 16x + 20 .

Problem : What is 2x 4 +8x 3 +2x 2 - 3x + 18 divided by x + 2 ?.

2x 3 +4x 2 - 6x + 9 .

Problem : What is x 4 -7x 3 +10x 2 + 4x - 20 divided by x - 5 ?

x 3 -2x 2 + 4 .

Problem : What is 3x 5 +15x 4 +6x 3 -18x 2 + 75x + 63 divided by 3x + 9 ?

x 4 +2x 3 -4x 2 + 6x + 7 .

Problem : What is x 5 +8x 4 +12x 3 - 8x - 48 divided by x + 6 ?

x 4 +2x 3 - 8 .

Problem : Is any of the following a factor of x 4 + x 3 -13x 2 - x + 12 ? a) x - 2
b) x + 4
c) x - 3
d) x + 3
e) x - 1
f) x

a) No.
b) Yes.
c) Yes.
d) No.
e) Yes.
f) No.

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