# College Algebra Problems With Answers sample 6 : Polynomials

 A set of college algebra problems on multiplying, dividing and finding polynomials are presented. The solutions are at the bottom of the page. Find the product of the polynomials P(x) = 2x 2 - 3x and Q(x) = 3x 2 + x - 5 Find the quotient and the remainder when polynomial P(x) = 2x 4 - x 3 -3x 2 + 7x - 13 is divided by Q(x) = x 2 - 4 Find the fourth degree polynomial P(x) whose graph is shown below. . Find the remainder if 4 x 200 + 5 x 95 - 4 x 21 + 2x - 6 is divided by x - 1 Find the third degree polynomial with leading coefficient -2 and having zeros 1, -2 and 3. Find all zeros of the polynomial P(x) = 3x 4 + 26 x 3 + 74 x 2 + 74 x + 15 knowing that P(x) has two rational zeros. Polynomial P(x) = x 3 + x 2 + c x + d has x - 2 as a factor and when divided by x - 1, the remainder is equal to 3. Find the constant c and d. P(x) is an even fourth degree polynomial function such that P(-2) = 0, P(x + 3) has a zero at x = 4 and P(0) = -9. Find P(x). The polynomial P(x) = 2 x 4 + 3 x 3 - 16 x 2 - 17 x + 12 has zeros at x = 1/2 and x = -3. Find the other zeros. Factor the following polynomials: a) f(x) = x 3 - x 2 - 4 x + 4 b) f(x) = 2 x 2 - x 3 c) f(x) = x 2 - 2 x 4 d) f(x) = -(x 2 - 2 x - 3) 2 e) f(x) = x 4 + 3 x 3 + 3 x 2 + x A polynomial of degree 4 has a negative leading coefficient and simple zeros (i.e. zeros of multiplicity 1) at x = 2, x = -2, x = 1 and x = - 1. Is the y intercept below the x axis or above the x axis? Match the function to the graph. 1) f(x) = (x + 1)(x - 1) 2(x + 2) 2 2) f(x) = -(x + 1)(x - 1) 4 3) f(x) = (x + 1)(x - 1) 3(x - 3) 4) f(x) = (x + 1) 2(x - 1) 3 . Give four different reasons why the graph below cannot possibly be the graph of p(x) = x 4 - x 2 + 1. . The graph of polynomial f is shown below. a) Is the degree of f even or odd? b) Is the leading coefficient negative or positive? c) Can you find the degree of f from the graph?Explain your answer. . If the polynomial 3x3 + qx2 + px + 7, where q and p are real numbers, is divided by x2 - 1, the remainder is 5x + 4. Find q and p.