Polynomial Test 2020-21

Name: ____________________________________ BlueTest – ___________ Score________ Part I Questions 40 2 pts 1. The power function y  axb is shown graphed below. Which of the following must be true about the values of a and b? (1) a must be even and b must be odd (2) a must be odd and b must be negative (3) a must be positive and b must be even (4) a must be negative and b must be even __________________________________________________________________________________________ 2pts 2. Which of the following is equivalent to x2 100 for all values of x, where x  10 ? 2x  20 (1) x 10 (3) x  5 2 2 (2) x  5 (4) x  50 2 10 __________________________________________________________________________________________ 4 pts 3. The cubic polynomial shown below has zeroes at x  4 and x  2 only and passes through the point 2,8 . What is the lead coefficient of the polynomial?

2 pts 4. Which of the following is an example of an identity? (1) x2  2x  8   x  2 x  4 (2) 2x  x  3  5x 15  2x  5 x  3 (3) x2  9   x  32  (4) x3  8   x  2 x2  4 __________________________________________________________________________________________ 2 pts 5. At which of the following values of x is the rational expression x2  2x  3 undefined? 2x2  x 10 (1) x  1 (3) x  2 1 2 (2) x  5 1 (4) x  3 4 __________________________________________________________________________________________ 4 pts 6. Factor completely: 2x4 – 8x3 – 32x2 + 128 __________________________________________________________________________________________ 4 pts 7. Algebraically, determine if (x + 3) is a factor of 2x3 – 4x2 – 7x – 10. Explain your reasoning. __________________________________________________________________________________________ 4 pts 8. Express the following division problem in simplest terms. 1 9x2 2  15x  5 3x2  7x  x2  5x 14

4 pts 9. The graph of a polynomial is shown below. a. What is the exponent of this power function? b. Is the lead coefficient positive or negative? Explain. __________________________________________________________________________________________ 4 pts 10. If f(x) = 3x3  4x  6 , what is the remainder of f(x)  (x+2)? __________________________________________________________________________________________ 4 pts 11. A quartic polynomial p(x) is shown graphed below, with the coordinate (-2,-144). Based on this graph, state the equation of p(x). You DO NOT need to distribute the lead coefficient. You do need to multiply the factors into a polynomial. __________________________________________________________________________________________ 4 pts. 12. Solve the following equation for all value(s) of x. x 1  1 4  x2 28 x3 x  x 12