Divide using long division. State the quotient, q(x), and the remainder, r(x). 5x - 8x- 2+x+7 5x~ + 2x + 7 5x" - 8x~ + x+ 7 5x~ + 2x + 7 5x~ + 2x + 7 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)Use synthetic division to find the quotient and the remainder. 4x" + 29x + 29x - 15 x+6 The quotient is (Use integers or fractions for any numbers in the expression. Do not factor.) The remainder is (Type an integer or a simplified fraction.)Find all rational zeros of the given polynomial function. fix) = x" - 10x~ + 23x - 14 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (O A. The set of rational zeros of f(x) is (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. The given function has no rational zeros.Find all rational zeros of f. Then (if necessary) use the depressed equation to find all roots of the equation f(x) = 0. 2x - 5x- - 5x - 1 =0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { (Type an exact answer, using radical as needed. Type an integer or a fraction. Use a comma to separate answers as needed. ) O B. There are no real zeros.Find a polynomial P(x) with real coefficients having a degree 4, leading coefficient 4, and zeros 3 - i and 3i. P(x) = (Simplify your answer.)Find the oblique asymptote of the graph of the rational function and sketch the graph the rational function. 21. Find the oblique asymptote of the graph of f. Select the correct choice below and ll in any answer boxes within your choice. [:1 A. y = [:1 B. There is no oblique asymptote. Sketch the graph the rational function. Choose the correct graph below. [:1 A. [:1 B. Q Q Q - q _ i3 F3. Suppose q is directly proportional to the square root of h and inversely proportional to the cube of j, and q = 1 q = 24 when h = 4 and j = 2. Find q when h = 4 and j = 312 Let f(x) = 2+aekx with f(0) = 3 and f(1) = - 2 Find a and k and then evaluate the function f(3). The value of a is .(Type an integer or decimal rounded to three decimal places as needed.) The value of k is . (Type an exact answer in simplified form. Type an integer or a fraction.) f(3 ) (Type an integer or decimal rounded to three decimal places as needed.)\fNegatlve ions, designated by the notation [OH1 are always present in any acid or base. The concentration, [OH _ :l of these ions is related to [H +] by the equation [OH fl - [H +] =10 _ H moles per liter. Find the concentrations of [0H _] and [H +] in moles per liter for the substances with the given pH value. pH=4 The concentration of [H1 is moles per liter. (Type your answer using exponential notation ] The concentration of [OH1 is mola per liter (Type your answer using exponential notation ]