(Medium)Use synthetic division to do the following for and the given value of p(x) c: Divide by = p(x) d(x) x c. − Rewrite in + form. p(x) d(x)q(x) r(x) Evaluate at = p(x) x c. = + 4x4 2x3 7x2 + 3x 5; = p(x) x5 c − − − −3 = 2x6 4x4 5x3 + 5; = 2 p(x) x c − − − = 2x4 + 3x3 + 2x2 1; = p(x) c − −1 Do the following for each polynomial: Use the Rational Zero Theorem to determine all possible rational zeros Use Descartes’s rule of signs to determine possible combinations of positive and negative zeros Factor the polynomial Sketch the graph (Medium)p(x) = 7x + 6 x3 − (Medium)p(x) = + 4x2 6 x −x3 − − (Medium)p(x) = 6x3 + 17x2 + 10 x − (Medium)p(x) = 6x3 + 5x 2 x2 − − (Hard)p(x) = + 4x3 3x2 10x + 8 x4 − − (Hard)p(x) = + 5x3 + 6x2 20x + 8 −2x4 − (Hard)p(x) = 3x4 + 7x2 4 x5 x3 − − − (Hard)p(x) = 2x6 13x4 + 13x3 + 19x2 32x + 12 x5 − − − (Medium) Find the least integer upper bound and the greatest integer lower bound for the real zeros of obtained by using the Upper and Lower Bounds Theorem. p(x), = 3x2 2x + 5 p(x) x4 − − = + 3x3 4x2 4 p(x) −2x5 − −
(Medium)Use synthetic division to do the following for p(x) and the given value of c: Divide p(x) by d(x) = x − c. Rewrite p(x) in d(x)q(x) + r(x) form. Evaluate p(x) at x = c. p(x) = x5 + 4x4 − 2x3 − 7x2 + 3x − 5; c = −3 p(x) = 2x6 − 4x4 − 5x3 + x − 5; c = 2 p(x) = 2x4 + 3x3 + 2x2 − 1; c = −1 Do the following for each polynomial: Use the Rational Zero Theorem to determine all possible rational zeros Use Descartes’s rule of signs to determine possible combinations of positive and negative zeros Factor the polynomial Sketch the graph (Medium)p(x) = x3 − 7x + 6 (Medium)p(x) = −x3 + 4x2 − x − 6 (Medium)p(x) = 6x3 + 17x2 + x − 10 (Medium)p(x) = 6x3 + x2 − 5x − 2 (Hard)p(x) = x4 + 4x3 − 3x2 − 10x + 8 (Hard)p(x) = −2x4 + 5x3 + 6x2 − 20x + 8 (Hard)p(x) = x5 − 3x4 − x3 + 7x2 − 4 (Hard)p(x) = 2x6 − x5 − 13x4 + 13x3 + 19x2 − 32x + 12 (Medium) Find the least integer upper bound and the greatest integer lower bound for the real zeros of p(x), obtained by using the Upper and Lower Bounds Theorem. p(x) = x4 − 3x2 − 2x + 5 p(x) = −2x5 + 3x3 − 4x2 − 4