Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: of p. √ 3 29 5. Find a quadratic polynomial with integer coefficients which has x = ± as its real zeros. 5 5 206 3.2.2 Polynomial Functions Answers 1. (a) 5x4 − 3x3 + 2x2 − 1 = (x2 + 4)(5x2 − 3x − 18) + (12x + 71) (b) −x5 + 7x3 − x = (x3 − x2 + 1)(−x2 − x + 6) + (7x2 − 6) 9 (c) 9x3 + 5 = (2x − 3)( 2 x2 + 27 4x + 81 8) + 283 8 (d) 4x2 − x − 23 = (x2 − 1)(4) + (−x − 19) 2. (a) p(−1) − 180 (b) p(8) = 0 (c) p( 1 ) = 2 825 32 (d) p( 2 ) = 0 3 (e) p(0) = 48 (f) p(− 3 ) = 0 5 3. (a) x3 − 6x2 + 11x − 6 = (x − 1)(x − 2)(x − 3) (b) x3 − 24x2 + 192x − 512 = (x − 8)3 (c) 4x4 − 28x3 + 61x2 − 42x + 9 = 4(x − 1 )2 (x − 3)2 2 2 (d) 3x3 + 4x2 − x − 2 = 3(x − 3 )(x + 1)2 (e) x4 − x2 = x2 (x − 1)(x + 1) √ √ (f) x2 − 2x − 2 = (x − (1 − 3))(x − (1 + 3)) 3 (g) 125x5 − 275x4 − 2265x3 − 3213x2 − 1728x − 324 = 125(x + 5 )3 (x − 6)(x + 2) 4. Something like p(x) = −(x + 2)2 (x − 3)(x + 3)(x − 4) will work. 5. q (x) = 5x2 − 6x − 4 3.3 Real Zeros of Polynomials 3.3 207 Real Zeros of Polynomials In Secti...
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