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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