1. Let P(x) = 2x +15x3 +31x? + 20x +4 %3D (*+:) is a factor of...

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1. Let P(x) = 2x +15x3 +31x? + 20x +4 %3D (*+:) is a factor of P(x). (a) Determine whether (2) (b) Find all the possible rational zeros of P(x) by using the Rational Zeros Theorem. (2) (c) Solve P(x) =0. (5) 2. Use Descartes' Rule of Signs to determine the possible number of positive, negative and imaginary zeros of P(x). P(x) = x6 - 4x5 – 2x* + 10x3 – 11x2 + 14x – 8. (4) 3. Let P(x) = x* – 2x3 + x2 - 9x + 2. (a) Use the Upper and Lower Bounds Theorem to show that the real zeros of P(x) lie between -2 and 3. (4) (b) Use the Rational Zeros Theorem and synthetic division or the Factor Theorem to show that the equation P(x) = 0 has no rational roots. (5) 1. Let P(x) = 2x +15x3 +31x? + 20x +4 %3D (*+:) is a factor of P(x). (a) Determine whether (2) (b) Find all the possible rational zeros of P(x) by using the Rational Zeros Theorem. (2) (c) Solve P(x) =0. (5) 2. Use Descartes' Rule of Signs to determine the possible number of positive, negative and imaginary zeros of P(x). P(x) = x6 - 4x5 – 2x* + 10x3 – 11x2 + 14x – 8. (4) 3. Let P(x) = x* – 2x3 + x2 - 9x + 2. (a) Use the Upper and Lower Bounds Theorem to show that the real zeros of P(x) lie between -2 and 3. (4) (b) Use the Rational Zeros Theorem and synthetic division or the Factor Theorem to show that the equation P(x) = 0 has no rational roots. (5)