please help with these questions

3 3 Fill in each blank so that the resulting statement is true. In the following long division problem, the first step has been completed. 4x2 5x - 4)20x3 + 8x2 - 8x + 12 The next step is to multiply the quotient and the divisor which obtains Write this result below The next step is to multiply the quotient and the divisor , which obtains Write this result below. 8 Fill out each boxUse the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) 23x4 + 3x3 +16x2 + 2x 6 Choose the answer below that lists all possible rational zeros. OA. 11 11 11 3 3 1133 ,, ., 2,2, 6.6, 3,3. 2.2 B. 11 11 11 1.1,2.2,3.3,6,6,2,2.3.3:6'6 0c. 11 22 1.1,2.2,3.3,6,6,3,3.3.3 OD. 11 11 11 2 2 3 3 "1172273376?\"212*ale" 33: 3,3: 2,2 Fill in each blank so that the resulting statement is true. Consider the following long division problem. 4x2)12x3+6x2+11x3 Begin the division process by dividing by . which obtains _ Write this result above in the dividend. Begin the division process by dividing by , which obtains _ Write this result above in the dividend. (3/ Use Gaussian elimination to nd the complete solution to the following system of equations, or show that none exists. x+ y+ 221 x+3yQz=5 2x y?z= 0 Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. A- There is one solution. The solution set is {( , , }. (Simplify your answers.) O 3- There are innitely many solutions. The solution set is {[ , Hz]} where z is any real number. (Type expressions using 2 as the variable. Use 'ntegers or fractions for any numbers in the expressions.) O C. There is no solution. The solution set is Q). Given the equation x4 + 4x3 3x2 716X 4 : 0, complete the following. a. List all possible rational roots. I). Use synthetic division to test several possible rational roots in order to identify one actual root. c. Use the root from part (b) to solve the equation. a. List all rational roots that are possible according to the Rational Zero Theorem. 7 1,1, 7 2,2, 7 4,4 (Use commas to separate answers as needed.) b. Use synthetic division to test several possible rational roots in order to identify one actual root One rational root of the given equation is 2 . (Simplify your answer.) c. Use the root from part (b) to solve the equation. The solution set is . (Simplify your answer. Type an exact answer' using radicals as needed. USe integers or fractions for anyr numbers in the expression. Use commas to separate answers as needed.) 794/ Find an nthdegree polynomial function with real coefcients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and \\ierifyl the real zeros and the given function value. n=3; 4 and 2 i' are zeros; f(1)= 15 (T f(X) = (Type an expression using x as the variable. Simplify your answer.) 7M Find an nth-degree polynomial function with real coefcients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and lhe given function value. n=4; 71, 5. and2+3iarezeros; f(1): 80 fix} 2 (Type an expression using x as the variable. Simplify your answer.)