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Operations with polynomials
1. （6𝑡 4 − 𝑡 +1）－（6𝑡 3 − 4𝑡）
Which of the following expressions is equivalent to the above expression?
A. 6𝑡 4 − 6𝑡 3 + 3𝑡 + 1
B. 6𝑡 4 − 6𝑡 3 − 5𝑡 + 1
C. 3t+1
D. -5t+1
Correct Answer: A Difficult Level: 3
2. Which of the following expressions is equivalent to the product of (𝑓 2 −2) and (𝑓 7 +
2𝑓 5 + 4𝑓 3 + 8𝑓)?
A. f(-2𝑓 8 − 2𝑓 6 − 4𝑓 4 − 8𝑓 2 − 16)
B. f(-2𝑓 8 − 4𝑓 6 − 8𝑓 4 − 16𝑓 2 )
C. f(𝑓 13 + 2𝑓 9 − 2𝑓 6 + 4𝑓 5 − 4𝑓 4 − 8𝑓 2 + 8𝑓 − 16)
D. f(𝑓 8 − 16)
Correct Answer: D
Difficult Level: 3
3.P(x) = 3𝑥 2 + 4𝑥 − 5 𝑎𝑛𝑑 𝑄(𝑥) = 7𝑥 3 − 2𝑥 − 5
Which of the following expressions is equivalent to P(x)-Q(x)?
A. −7𝑥 3 + 3𝑥 2 + 6𝑥
B. −7𝑥 3 + 3𝑥 2 + 6𝑥-10
C.−4𝑥 2 + 6𝑥
D. −4𝑥 2 + 6𝑥 − 10
Correct Answer: A Difficult Level: 3
4. Let α(u)=(u+2u2+3u3) and β(u)=(1+u). Which of the following expressions is
equivalent to α(u)⋅β(u)?
A. u+2u2+5u3+3u4
B. 1+2u+2u2+3u3
C. u+5u6+7u8
D. 1+3u3+4u4
Correct Answer: A Difficult Level: 3
5. (−5z)−(2−z)⋅(3−z)
Which of the following expressions is equivalent to the above expression?
A. −z2−10z−6
B. −z2−4z+6
C. −z2−6
D. z2−10z−6
Correct Answer: C Difficult Level: 3
7
7
4
3
3
3
6. (s−2)+( s3+ s2−7s+ )
Which of the following expressions is equivalent to the above expression?
1
A. (7s3+7s2−18s−2)
3
B.
1
(7s3+7s2−6s−2)
3
1
C. (7s3+7s2−18s+2)
3
D.
1
(7s3+7s2−6s+2)
3
Correct Answer: A
1
1
4
2
Difficult Level: 4
7. (−2j2 )⋅ +( 𝑗 2 − 1)
Which of the following expressions is equivalent to the above expression?
A. -1
B.
3 2
𝑗
8
−1
1
1
2
2
C. ( 𝑗 + 1)( 𝑗 − 1)
D. (j+1) (j-1)
Correct Answer: A
Difficult Level: 4
1
8. What is the product of (1−p) and ( −p), all reduced by p?
2
1
(1-5p+2p2)
2
A.
B.
1
2
(2-5p+2p2)
1
C. (1-3p+2p2)
2
1
D. (2-3p+2p2)
2
Correct Answer: A
Difficult Level: 4
2
1
1
1
3
2
3
4
9. What is the sum of (w6+ w2) and ( w6+ w2+ )?
1
1
1
2
3
4
A. ( w6+ w2- )
1
1
2
4
B. ( w6+w2+ )
3
1
1
2
3
4
C. ( w6+ w2− )
3
1
2
4
D. ( w6+w2+ )
Correct Answer: D
Difficult Level: 4
1
10. f (x)= ( x−1) g(x)= (x3+2x2+4x+8)
2
Which of the following expressions is equivalent to f(x)g(x)?
A.
1 4
x
2
B.
1 4
x +x3+2x2+4x-8
2
−8
1
C. − 2 x4 -x2-2x-4
1
D.− x 4 +x2+2x-4
2
Correct Answer: A
Difficult Level: 4
11. 2x(x−2)+3(4−x2)
Which of the following is equivalent to the above expression?
A. (6+x) (2-x)
B. (x-6) (x+2)
C. x2+10
D.x2-4x+12
Correct Answer: A
Difficult Level: 4
12. (3y−2) (y+a)=3y2+by−24
If the above equation is true for all values of y, where a and b are constants, which of the
following is the value of b?
A. -38
B. 12
C. 34
D. 36
Correct Answer: C
Difficult Level: 4
13. Which of the following is the product of w+2, 2w-5,w+2,2w−5, and 3w+43w+4?
A. 6w3-40
B. 6w3+40
C. 6w3+5w2-34w-40
D. 6w3+11w2-26w-40
Correct Answer: C
Difficult Level: 4
14. P(x)=g2+10g+25 and Q(x)=g+5. What is P(x)⋅Q(x)?
A. (g3+5)2
B. (g2+5)2
C. (g+5)2
D. (g+5)3
Correct Answer: D
Difficult Level: 4
15. 4−4a−(5+a)(5−a)
Which of the following expressions is equivalent to the above?
A. (a-7)(-a+3)(a−7)(−a+3)
B. (-a+7)(a+3)(−a+7)(a+3)
C. (a-7)(a+3)(a−7)(a+3)
D. (a+7)(a-3)(a+7)(a−3)
Correct Answer: C
Difficult Level: 4
16. (−1−5n+an2)−(7n−4n2+9)=12n2−12n−10
If the equation above is true for all values of n, then which of the following is the
value of a?
A. 8
B. 12
C. 16
D. 19
Correct Answer: A Difficult Level: 3
17. Which of the following is equivalent to 18 more than the product of 9−6p and p2?
A. 3(7p+6)
B. -3p(2p-7)
C. (27-6p)(p-2)
D. (9-6p)(p+16)
Correct Answer: B Difficult Level: 3
18. (8c+5)3.Which of the following is equivalent to the above expression?
A. 512c2+125
B. (8c+5) (64c2-40c+25)
C. 128c3+1040c2+220c+625
D. 512c3+960c2+600+125
Correct Answer: D
Difficult Level: 3
2
1
3
9
19. b(− 𝑏 + 1)+ 6( b2 -21)
Which of the following expressions is equivalent to the above expression?
A. b - 20
B. b -126
C. (-
2
3
1
b2+7) ( b2 -21)
9
1
2
9
3
D. (b+6) ( b2-
b -20)
Correct Answer: B
Difficult Level: 3
20. Q(t)=2−0.3t+0.8t2 and R(t)=1.5t2+0.7t-6.3
Which of the following is equivalent to R(t)-Q(t)?
A. -0.7t2-t+8.3
B. -0.5t2+t-7.1
C. 0.7t2+0.4t-4.3
D. 0.7t2+t-8.3
Correct Answer: D
Difficult Level: 3
21. What is the sum of 3b(b-4)3b(b−4) and 6(b-8)6(b−8)?
A. 3b (1-2b-16)
B. 3b (b-2-16)
C. 3(b2-2b-16)
D. 3(b2-2-16b)
Correct Answer: C Difficult Level: 2
22. Which of the following expressions is equivalent to:
(4X3-5X)+(8X-3X3)
A. x3+3x
B. x3-3x
C. 7 x3-3x
D. 7x3+3x
Correct Answer: A
Difficult Level: 2
23. Which of the following expressions is equivalent to (3c-4c2+c3) – (5c2+8c3-6c)
A. 7c3 +9c2 -3c
B. 7c3 +c2 -3c
C. -7c3 +c2 +9c
D. -7c3 -9c2 +9c
Correct Answer: D
Difficult Level: 2
24. Which of the following is equivalent to (8r4+4r2+2r)-(8r4+4r2+1) (8r4+4r2
+2r)−(8r4+4r2+1)?
A. 8r2+2r+1
B. 8r2+3r
C. 2r-1
D. r
Correct Answer: C
25. What is the product of
Difficult Level: 2
(x+6) and (x+1)?
A. x2+7x+6
B. x2+6x+7
C.8x+6
D. 7x+7
Correct Answer: A
Difficult Level: 2