02/04/2020 Algebra II(Senior Class Math Study by Topics ) 02/04/2020 0Comments by Gate Academy Welcome to your Algebra II(Senior Class Math Study by Topics ) NAME EMAIL PHONE NUMBER 1. Resolve into partial fractions. 2/(x-1) + 3/(x+1) + 1/(x+3) 2/(x-1) - 3/(x+1) + 1/(x+3) 2/(x-1) - 1/(x+1) + 1/(x+3) 2/(x-1) - 3/(x+1) + 2/(x+3) 2. Expand completely (1 - 3x)5 in ascending powers of x. 1 - 5x² + 270x3 + 405x4 - 243x5 1 - 15x + 90x² + 270x3 + 405x4 - 243x5 1 - 5x + 67x² + 270x3 + 405x4 - 243x5 1 - 5x + 67x² + 270x3 3. Find the remainder when4x³+ 5x²- 4x+ 20 is divided by x+4 140 -140 0 1 4. Given that (1 + 3x)10 = 1 + Px +Qx² + Rx³...find the values of the integers P, Q and R, respectively. 98, 755, 8689 30, 405, 3240 409, 67, 675 6, 54, 4754 5. Resolve into partial fractions 1/(x+2) - 3/(2-x) 1/(x+2) - 2/(4-x) 2/(x-3) + 2/(2-x) 7/(x+3) - 4/(x+2) 6. Factorize the polynomial x 3 - 1 x-1 (x - 1)(x² + x + 1) (x-1)² 2x+1 7. Given that (1 + 5x)4 = 1 + Px + Qx² + Rx³ + ...find the value of P - 2Q + 3R 220 120 1220 20 8. Subtract the polynomials: (-x2 + 5 x) - (6 x2 + x - 2) -7x²+4x+2 -5x²+6x+2 5x²+6x-2 5x²+6x 9. If (1 + px)n = 1 + 2x - 3x² + ... where Px<1, determine the values of p and n, respectively. 2/5, 5 5, 2/5 7, 3/4 3/4, 7 10. Find the binomial expansion of (1.04)5 1.2167 1.5332 1.4633 2.4342 11. Expand (1-x)³, using binomial theorem. Hence find the value of (0.999)³ correct to five decimal places. 1 - 3x + 3x² - x³, 0.99700 1 - 3x + 3x² - x³, 0.10 1 - 3x + 3x² - x³, 0.997 1 - 3x + 3x² - x³, 1 12. What is:(9 x - 6) + (- 5x + 7) 4x + 1 4x + 13 -4x - 1 14x + 1 13. Decompose into partial fractions : (5x2 + 12x + 3) / x(x + 1)2 2/(x+7) - 3/x²- 2/(x + 1)² 3/x + 2/(x + 1) + 4/(x + 1)² 4/(x + 1)² +3/x x + 2/(x + 1) 14. Find the remainder when 3x³ + 5x² - 11x + 4 is divisible by x + 3 0 -1 2 1 15. Subtract the polynomials: (9 x - 6) - (- 5x + 7) 4x + 1 -4x - 13 -4x + 13 14x - 13 16. Add the polynomials: (- 7 x2y + xy + 3x + 2) + (5 x2y - 5 xy - 6x - 7) 2x²y + 4 xy + 3x + 5 2x²y +4xy-3x-5 -2x²y-4xy-3x-5 -2x²y-4xy +3x+5 17. Decompose into partial fractions : (5x + 10) / x(x + 5) 2/x + 3/(x + 5) 3/ (x+5) x/2 + 3/(x+3) x/2 18. If find P + Q + R. 3 1 4 2 19. If (x-3) and (x+5) are factors of the expression x³ + mx² - nx - 45, what is the product of m and n 55 35 67 45 20. What is the common factor to the expressions y²-y, 2y²+y-1 and y²-1? y-1 None y y+1 21. Find the coefficient of x³ in the binomial expansion of (2-5x)7 -30000 50000 12000 -70000 22. The graph of a cubic polynomial y = a x 3 + b x 2 + c x + d is shown below. Find the coefficients a, b, c and d. a = 2 , b = 1/4, c = 3/2 and d = 1 a = 2 , b = 10, c = 3/2 and d = 1 a = 1/2 , b = 5, c = -3/2 and d = 1/3 a = 1/2 , b = 0, c = -3/2 and d = 1 23. Find the remainder when 12x4-9x2-2x-1 is divided by 2x+1 1+x 0 x-1 1/x 24. Find the third term in the expansion of (1-2x)10 180x² 12 123x² 20x 25. Find the fourth term in the expansion of (1+x)15 13x³ 1 13 455x³ 1 out of 25