Name: ________________________ Class: ___________________ Date: __________
Chapter 3 Test Review
Short Answer
1. Find the product −4c 5 d (−2c 5 d 4 − 4d 4 ).
2. Find the product −x 4 y 4 (−5x 3 − 5x y 3 ).
3. Add. Write your answer in standard form.
(5a 5 − a 4 ) + (a 5 + 7a 4 − 2)
4. Add. Write your answer in standard form.
(7b 5 − b 3 ) + (b 5 + 6b 3 − 1)
5. Add. Write your answer in standard form.
(2e 3 − e 2 ) + (e 3 + 4e 2 − 4)
Ê
ˆÊ
ˆ
6. Find the product ÁÁ 7x + y 2 ˜˜ ÁÁ 7x − y 2 ˜˜
Ë
¯Ë
¯
7. Find the product 2c d 4 (−4c 6 d 5 − c 3 d ).
8. Determine whether the binomial (x + 5) is a factor of the polynomial P (x) = x 3 + 4x 2 − 7x − 10.
9. Determine whether the binomial (x + 3) is a factor of the polynomial P (x) = x 3 − x 2 − 8x + 12.
10. Find the product (5x − 3) (x 3 − 5x + 2).
11. Determine whether the binomial (x − 4) is a factor of the polynomial P (x) = 5x 3 − 20x 2 − 5x + 20.
12. Factor the expression 54x 7 + 128x 4 y 3 .
13. Factor x 3 + 5x 2 − 9x − 45.
14. Factor x 3 + 7x 2 − 36x − 252.
15. Factor the expression 81x 6 + 24x 3 y 3 .
16. Solve the polynomial equation 3x 5 + 6x 4 − 72x 3 = 0 by factoring.
17. Solve the polynomial equation 5x 5 − 25x 4 + 30x 3 = 0 by factoring.
1
ID: A
Name: ________________________
ID: A
18. Identify the leading coefficient, degree, and end behavior of the function P(x) = –5x 4 – 6x 2 + 6.
19. Identify the leading coefficient, degree, and end behavior of the function P(x) = 2x 4 – 5x 2 + 9.
20. Identify the leading coefficient, degree, and end behavior of the function P(x) = 9x 5 – 7x 3 – 2.
21. Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
22. Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
2
Name: ________________________
ID: A
23. Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
2
24. Sketch the graph of the following polynomial f(x) = (x + 2) (x − 3)
3
3
Name: ________________________
ID: A
3
25. Sketch the graph of the following polynomial f(x) = −x (x − 2) (x + 3)
4
ID: A
Chapter 3 Test Review
Answer Section
SHORT ANSWER
1. 8c 10 d 5 + 16c 5 d 5
2. 5x 7 y 4 + 5x 5 y 7
3. 6a 5 + 6a 4 − 2
4. 8b 5 + 5b 3 − 1
5. 3e 3 + 3e 2 − 4
6. 49x 2 − y 4
7. −8c 7 d 9 − 2c 4 d 5
8. (x + 5) is a factor of the polynomial P (x) = x 3 + 4x 2 − 7x − 10.
9. (x + 3) is a factor of the polynomial P (x) = x 3 − x 2 − 8x + 12.
10. 5x 4 − 3x 3 − 25x 2 + 25x − 6
11. (x − 4) is a factor of the polynomial P (x) = 5x 3 − 20x 2 − 5x + 20.
12. 2x 4 (3x + 4y)(9x 2 − 12xy + 16y 2 )
13. (x + 5)(x − 3)(x + 3)
14. (x + 7)(x − 6)(x + 6)
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
3x 3 (3x + 2y)(9x 2 − 6xy + 4y 2 )
The roots are 0, –6, and 4.
The roots are 0, 3, and 2.
The leading coefficient is –5. The degree is 4.
As x →−∞, P(x) →–∞ and as x →+∞, P(x) →–∞
The leading coefficient is 2. The degree is 4.
As x →−∞, P(x) →+∞ and as x →+∞, P(x) →+∞
The leading coefficient is 9. The degree is 5.
As x →−∞, P(x) →–∞ and as x →+∞, P(x) →+∞
The degree is odd, and the leading coefficient is positive.
The degree is even, and the leading coefficient is negative.
The degree is odd, and the leading coefficient is negative.
Various
Various
1