Welcome to your Algebra II(Senior Class Math Study by Topics ) NAME EMAIL PHONE NUMBER 1. Decompose into partial fractions : (2x2 + 6x - 2) / (x3 - 1) 2/ x²+1 2/(x - 1) + 4/(x²+ x + 1) 4/ 3x+2x² -1 2/(x² - 1) + 4/(x2 + 2x + 1) 2. Given that (1 + 3x)4 = 1 + Px + Qx² ...find 3P + 2Q. 144 24 12 72 3. Given thatwhere A and B are constants, find the value of (A + B) 3 1 2 4 4. Express in partial fractions. 4/(x+3) + 2/(x+1) 5/(x-3) + 3/(x+4) 2/(x-4) + 3/(x-6) 1/(x+3) + 4/(x-4) 5. Subtract the polynomials: (-x2 + 5 x) - (6 x2 + x - 2) -5x²+6x+2 5x²+6x 5x²+6x-2 -7x²+4x+2 6. Factorize the polynomial x 3 - x 2 - 25x + 25 x²-1(x-5) (x - 1)(x + 5)(x - 5) (x - 1)(x + 5)² (x-5)² 7. If (x-1) and (x+1) are both factors of the equation x³ +px +qx + 6 = , evaluate p and q, respectively -1, 4 3, -4 1, -3 -6, -1 8. Given that find the value of Q 1 2 1/2 1/3 9. Find the third term in the binomial expansion of (2-a)10 45332a 45332a² 11520a² 11520a 10. Use binomial theorem to expand (1 - 4x)³ in ascending powers of x 1 - 2x + 8x2 + 14x3 1 - 12x + 48x2 1 - 12x + 48x2 + 64x3 1 - 12x + 64x3 11. When the polynomial x³ + mx² + 4x + 2 is divided by x + 2.What is the value of m? 5 2 3 4 12. If 9x² + 6xy + 4y² is a factor of 27x³ - 8y², find the other factor 4x-5y x+3y 3x-2y x+y 13. Find the remainder when 12x4-9x2-2x-1 is divided by 2x+1 1/x 0 1+x x-1 14. Factorize the polynomial x 3 - 1 (x - 1)(x² + x + 1) (x-1)² x-1 2x+1 15. Given that (1 + 5x)4 = 1 + Px + Qx² + Rx³ + ...find the value of P - 2Q + 3R 20 220 120 1220 16. Iffind P+ Q 24/362 51/192 61/678 41/187 17. Using the binomial theorem in the expansion of (x + 3/x)4, find the term which is independent of x. 66 74 54 64 18. What is:(9 x - 6) + (- 5x + 7) 4x + 1 -4x - 1 4x + 13 14x + 1 19. Use the binomial theorem to expand (1 + 4x)4. Hence, find the value of (1.04)4 correct to 4 decimal places 1 + 16x + 96x² + 256x4; 1.16 1 + 16x + 96x² + 256x3 + 256x4; 1.1699 1 + 96x² + 256x3 + 256x4; 1.169 1 + 16x + 96x² + 256x3 + 256x4; 1.1 20. Add the polynomials: (xy + 3x + 2) + (3x2 + y) 3x²+5xy+2 3x²+xy+3x+y+2 3x²+4xy+2 3x²+2xy+3x+2 21. Decompose into partial fractions : (8x + 14) / (x + 1)(x + 5) 3/(2(x + 5)) + 13/(2(x + 6)) 3/2(x+5) 3/(2(x + 1)) + 13/(2(x + 5)) 13/(2(x + 5)) 22. Find the fourth term in the expansion of (1+x)15 13x³ 455x³ 1 13 23. Find the binomial expansion of (3.2)4 293.42 145.34 104.86 123.45 24. Factorize completely 3x3 + 4x2 – 13x + 6 completely, given that x-1 is a factor 2x-5 (x-1)(x+3)(3x-2) (x+2)(3x-1) 3x+1 25. Expand (1 + x)5 in ascending powers of x. Without using any calculating device, estimate (1.1)5, giving your answer correct to 4 decimal places 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.61 1 + 5x + 10x3 + 5x4 + x5, 1.6105 1 + 5x + 10x2 + x5, 1.610534 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.6105 1 out of 25