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Algebra II: Polynomials

Problems

The Rational Zeros Theorem

Complex Zeros and the Fundamental Theorem of Algebra

Problem : Find all the rational zeros of P(x) = 6x 4 - x 3 -55x 2 + 9x + 9 .

x = - 3 , - , , 3 .

Problem : Find all the rational zeros of P(x) = 3x 4 +10x 3 -11x 2 - 10x + 8 .

x = - 4 , -1 , , 1 .

Problem : Find all the rational zeros of P(x) = 2x 4 + x 3 -14x 2 + 5x + 6 .

x = - 3 , - , 1 , 2 .

Problem : Factor completely: P(x) = 3x 3 +17x 2 + 5x - 25 .

P(x) = (3x + 5)(x + 5)(x - 1) .

Problem : Factor completely: P(x) = 4x 4 +13x 3 -49x 2 - 73x - 15 .

P(x) = (4x + 1)(x + 5)(x + 1)(x - 3) .

Problem : Factor completely: P(x) = 8x 4 +24x 3 -34x 2 - 6x + 8 .

P(x) = 2(2x + 1)(2x - 1)(x + 4)(x - 1) .

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