Test Name: Test 2 Fall 2014 PRACTICE

1. Solve the polynomial equation x2−6 x+12=0, by factoring or using the quadratic formula, making sure to identify all the solutions.

2. Solve the polynomial inequality ( x−5 ) ( x+3 ) (2−x )£ 0. Write your answer in interval notation.

3. Does the given value of x solve the polynomial equation?−54 x2+14 x=7 x3+16 ; x=−8

4. Determine the x-intercepts, the y -intercept and the correct graph of the polynomial function f ( x )=x2+2 x−3 . Write all points as ordered pairs, separate multiple answers with a comma, and select the graph from the options labeled (a) to (d) below.

Answer: A) YES B) NO

(a) (b) (c) (d)

x -intercepts: y -intercept:

5. Determine the x-intercepts, the y -intercept and the correct graph of the polynomial function f ( x )=x3+5 x2+4 x . Write all points as ordered pairs, separate multiple answers with a comma, and select the graph from the options labeled (a) to (d) below.

6. Determine the x-intercepts, the y -intercept and the correct graph of the polynomial function g ( x )=( x−2 ) ( x+1 ) (6−x ) . Write all points as ordered pairs, separate multiple answers with a comma, and select the graph from the options labeled (a) to (d) below.

7. Consider the following polynomial.g ( x )=2 x2+5 x−6

Step 1. Determine the degree and the leading coefficient of g ( x ).

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(a) (b) (c) (d)

x -intercepts: y -intercept:

(a) (b) (c) (d)

x -intercepts: y -intercept:

Degree: Leading Coefficient:

2

3

Step 2. Describe the behavior of the graph of g ( x ) as x ê±Ù .

8. Graph the following polynomial function.f ( x )=x2+4 x−5

Step 1. Plot the x-intercepts, if any, of this function on the graph. Indicate the number of x-intercepts.

Step 2. Sketch the general shape of the graph in each region.

g ( x )ê as x ê−Ù

g ( x )ê as x êÙ

A) none

B) one

C) two

D) three

E) four

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9. Use polynomial long division to rewrite the following fraction in the form q (x)+ r (x)d (x)

, where d (x ) is the denominator of

the original fraction, q (x) is the quotient, and r (x ) is the remainder.

x2+11 x−12x+6

10. Use polynomial long division to rewrite the following fraction in the form q (x)+ r (x)d (x)

, where d (x ) is the denominator of

the original fraction, q (x) is the quotient, and r (x ) is the remainder.

10x5+2 x4−24 x3−4 x2+8 x2 x3−4 x

11. Use synthetic division to determine if the given value for k is a zero of this polynomial. If not, determine p(k) .

p(x )=2 x3−6 x2−15x−25; k=5

12. Use the method of elimination to solve the following system of equations. If the system is consistent, express the solution as an ordered pair. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.

{−6 x−4 y ¿ 18x+7 y ¿ 35

13. Evaluate the determinant of the matrix.

A=[72 −6036 −30]

14. Use Cramer's rule to solve the system { x −¿11 y ¿ 5311 x +¿2 y ¿ −32 .

Indicate the number of solutions to this system. State the solution, if one exists, and if there are infinitely many solutions, express the solution set in terms of one of the variables.

Is k a zero of this polynomial? A) Yes B) No p(k)=¿

A) Consistent System B) Inconsistent System C) Dependent System

A) No Solution B) One Solution C) Infinitely Many Solutions

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15. Given the following matrices, if possible, determine A+B+C . If not, state "Not Possible".

A=[−3 9−3 92 −1] B=[−4 3

−2 7−8 2] C=[ 0 0

6 −6−4 4 ]

16. Given the following matrices, if possible, determine 3 A . If not, state "Not Possible".

A=[ 0 −9−8 16 5 ]

17. Given the following matrices, if possible, determine 3 A−5 B. If not, state "Not Possible".

A=[−10−1 ] B=[46 ]

18. Given the following matrices, if possible, determine AB. If not, state "Not Possible".

A=[1 −9 5 ] B=[6 −23 −30 −1]

19. Given the following matrices, if possible, determine BA. If not, state "Not Possible".

A=[−3 2−3 9] B=[ 9

−1−4 ]

20. Write the following system of equations as a single matrix equation.

{3 x −¿4 y ¿ −18 x +¿ y ¿ 6

6

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21. Find the inverse of the following matrix, if possible. Reduce all fractions to lowest terms.

A=[ 2 −5−1 6 ]

22. Solve the following system by the inverse matrix method, if possible. If the inverse matrix method doesn't apply, use any other method to determine if the system is inconsistent or dependent. Indicate the number of solutions to this system by selecting the appropriate response. State the solution, if one exists, and if there are infinitely many solutions, express the solution in terms of one of the variables.

{2 x −¿6 y ¿ 364 x +¿3 y ¿ −3

23. Solve the following nonlinear system algebraically. Be sure to check for non-real solutions.

{ y−7=2x3 x2+ y2=49

A) No Solution B) One Solution C) Infinitely Many Solutions

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