Find a polynomial with real coefficients that satisfies the conditions. (Easy)degree 4; zeros 1, -2, 3i (Easy/Medium) degree 5; 2 (mult. 2), -1, -1+2i degree 3; zeros 0, i; = 4 p(1) degree 4; -1 (mult. 2), 1-i; = p(2) −18 Given a zero of the polynomial, factor the polynomial into linear factors. (Medium) = 3x2 + 4x 2; 1 p(x) x3 − − (Medium) = + 5x2 + 17x + 13; -1 p(x) x3 (Hard) = 6x3 + 14x2 24x + 40; 2i p(x) x4 − − (Hard) = + 2x3 + 10x2 + 24x + 80; 1 + 3i p(x) x4 (Hard)Do the following for each polynomial: Factor into linear and irreducible quadratic factors. Completely factor into linear factors. = 3x3 + 26x2 22x 52 p(x) x4 − − − = 4x3 4x2 5x 3 p(x) x5 x4 − − − − − For each of the following, give an equation for each asymptote. Sketch the graph using the asymptotes and x-intercept(s), if any. (Easy) (Medium) (Medium) (Medium) (Medium) (Medium) (Hard) (Hard)
Find a polynomial with real coefficients that satisfies the conditions. (Easy)degree 4; zeros 1, -2, 3i (Easy/Medium) degree 5; 2 (mult. 2), -1, -1+2i degree 3; zeros 0, i; p(1) = 4 degree 4; -1 (mult. 2), 1-i; p(2) = −18 Given a zero of the polynomial, factor the polynomial into linear factors. (Medium) p(x) = x3 − 3x2 + 4x − 2; 1 (Medium) p(x) = x3 + 5x2 + 17x + 13; -1 (Hard) p(x) = x4 − 6x3 + 14x2 − 24x + 40; 2i (Hard) p(x) = x4 + 2x3 + 10x2 + 24x + 80; 1 + 3i (Hard)Do the following for each polynomial: Factor into linear and irreducible quadratic factors. Completely factor into linear factors. p(x) = x4 − 3x3 + 26x2 − 22x − 52 p(x) = x5 − x4 − 4x3 − 4x2 − 5x − 3 For each of the following, give an equation for each asymptote. Sketch the graph using the asymptotes and x-intercept(s), if any. (Easy) (Medium) (Medium) (Medium) (Medium) (Medium) (Hard) (Hard)