(Easy)Find the multiplicity of the given zero in the polynomial. = (x + 1)(x 3); = p(x) c − −1 = (x 2)3(x 5); = 2 p(x) c − − = 2x 8; = 4 p(x) x2 c − − = 4x + 4; = 2 p(x) x2 c − (Easy)Find a polynomial with the given conditions. (Answers may vary) degree 3, zeros -2, 0, 3 degree 3, zeros 0 (multiplicity 2) and 1 (Easy)Find the unique polynomial with the given conditions. degree 2, -3 and -1, leading coefficient = an −3 degree 3, zeros 2 (multiplicity 2) and -4, = 21 p(3) (Easy)Divide by using long division. p(x) d(x) = 6x4 4x3 + 3x2 14x + 2; = 3x 2 p(x) d(x) − − − = 2x3 5x2 + 1; = 3 p(x) d(x) x2 − − = 10x3 + + 18x + 2; = 2x2 + 4 p(x) x2 d(x) − x (Medium)Use synthetic division to do the following for and = p(x) d(x) 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. = 2x4 3x3 5x2 + 6; = 1 p(x) x d(x) x − − − − = 3x4 2x3 4x + 8; = + 2 p(x) d(x) x − − = 7x2 + 17x 20; = 4 p(x) x3 d(x) x − − −
(Easy)Find the multiplicity of the given zero in the polynomial. p(x) = (x + 1)(x − 3); c = −1 p(x) = (x − 2)3(x − 5); c = 2 p(x) = x2 − 2x − 8; c = 4 p(x) = x2 − 4x + 4; c = 2 (Easy)Find a polynomial with the given conditions. (Answers may vary) degree 3, zeros -2, 0, 3 degree 3, zeros 0 (multiplicity 2) and 1 (Easy)Find the unique polynomial with the given conditions. degree 2, -3 and -1, leading coefficient an = −3 degree 3, zeros 2 (multiplicity 2) and -4, p(3) = 21 (Easy)Divide p(x) by d(x) using long division. p(x) = 6x4 − 4x3 + 3x2 − 14x + 2; d(x) = 3x − 2 p(x) = 2x3 − 5x2 + 1; d(x) = x2 − 3 p(x) = 10x3 + x2 + 18x + 2; d(x) = 2x2 − x + 4 (Medium)Use synthetic division to do the following for p(x) and d(x) = x − 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) = 2x4 − 3x3 − 5x2 + x − 6; d(x) = x − 1 p(x) = 3x4 − 2x3 − 4x + 8; d(x) = x + 2 p(x) = x3 − 7x2 + 17x − 20; d(x) = x − 4