Algebra 2 Unit 6 Quiz 2

14. Select the correct equation represented by the synthetic division problem. -4| 1 8 14 -8 | -4 -16 8 |--------------- | 1 4 -2 0

(x'3+8x'2+14x-8)/(x+4)=x'2+4x-2

20. Select the correct equation represented by the synthetic division problem. 3| 1 1 -14 6 | 3 12 -6 |-------------- | 1 4 -2 0

(x'3+x'2-14x+6)/(x-3)=x'2+4x-2

3. Use the constant term and leading coefficient of each expression to list all its potential roots. Select all that apply. x⁵-2x⁴-5x³+9x²+2 Factors: 1,2,-1,-2 Factors of Leading Coefficient: 1,-1 Potential Roots:

±1 ±2

7. Divide using synthetic division. 1| 3 8 -2 5 | |------------ |

3x'2+11x+9 Remainder 14

5. Choose the best answer. The numerators of any rational roots of a polynomial will be the factors of the ___ term.

Constant

4. Use the constant term and leading coefficient of each expression to list all its potential roots. 3x'5-7x'4-5x'3+18x'2-5

Factor of Constant: e. ±1,±5 Factors of Leading Coefficient: b. ±1,±3 Potential Roots: a. ±1,±1/3,±5,±5/3

10. Choose the best answer. It is often useful to find the ___ of a polynomial in order to find its roots.

Factors

1. Choose the best answer. The points where the graph of the polynomial crosses the x-axis are called ___ number roots.

Real

11. Choose the best answer. The value of a polynomial at x=7 is the ___ when the polynomial is divided by x-7

Remainder

9. Choose the best answer. The denominators of any rational roots of a polynomial will be the factors of the ___ coefficient.

Leading

15. Choose the correct roots for each polynomial equation. x'3-7x+6=(x-1)(x+3)(x-2)

x=1,-3,2

6. Choose the best answer. A shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called ___ division.

Synthetic

16. Choose where the graphs of the polynomial functions would cross the x-axis. f(x)=x'2-8x+15

x=5,3

19. Choose where the graphs of the polynomial functions would cross the x-axis. f(x)=3x'2-12x-36

x=6,-2

13. Choose the best answer. The roots of a polynomial are values that make the polynomial equal ___.

Zero

18. Divide using synthetic division. -4| 1 7 2 -40 | | |------------- |

x'2+3x-10

17. Divide using synthetic division. 2| 1 2 -5 -6 | |------------- |

x'2+4x+3

12. Choose the correct roots for each polynomial equation. x'3+x'2-22x-40=(x+2)(x+4)(x-5)

x= -2,-4,5

8. Choose where the graphs of the polynomial functions would cross the x-axis. f(x)=x'2-4x-12

x=-2,6

2. Choose the correct roots for each polynomial equation. x'3+2x'2-23x-60= (x+3)(x+4)(x-5)

x=-3,-4,5