Welcome to your Algebra II(Senior Class Math Study by Topics ) NAME EMAIL PHONE NUMBER 1. Express in partial fractions. 2/(x-4) + 3/(x-6) 4/(x+3) + 2/(x+1) 1/(x+3) + 4/(x-4) 5/(x-3) + 3/(x+4) 2. Decompose into partial fractions : (5x + 10) / x(x + 5) x/2 x/2 + 3/(x+3) 3/ (x+5) 2/x + 3/(x + 5) 3. Find the remainder when4x³ + 5x² - 11x + 10 is divided by x+2 19 20 21 18 4. Subtract the polynomials: (xy + 3x + 2) - (3x2 + y) -3x²+3x-y+2 3x²+4xy+2 -3x²+xy+3x-y+2 5. Factorize the polynomial (x + 1) 2 - 4 (x - 1)(x + 3) (x²- 1)(x + 3) (x - 1)(x² + 3) (x² - 1)(x² + 3) 6. If (1 + 2x)6 = 1 + Px + Qx² + ...., find the values of the constant P and Q, respectively. 12, 60 10, 50 8, 55 14, 72 7. The graph of the polynomial y = a x 4 + b x 3 + c x 2 + d x + e is shown below. Find the coefficients a, b, c, d and e. a = -18, b =4, c = 14, d = 0, e = -2 a = -1 / 7, b = 1, c = 1, d = 0, e = -4 a = -1 / 8, b = 0, c = 1, d = 0, e = -2 a = 8, b = 0, c = 1, d = 10, e = 2 8. If the function f(x) = x³ + 2x² +qx - 6 is divisible by x + 1, find q 5 -2 1 -5 9. Find the roots of x³ + 2x² - 5x + 6 = 0 -1, -3, 2 1, -2, -3 -1, 3 1, 3, 2 10. Simplify a/(a-3)(a+7) a/(a-3)(a-7) a/(a+3)(a+7) (a+3)(a+7)/a 11. Iffind the values of the constants P and Q P = 3, Q = 2 P = 2, Q = 2 P = 1, Q = 2 P = 3, Q = 1 12. Find the term independent of x in (x + 3/x)8 5760 567 5670 56 13. If y + 1/y = 4, find y² + 1/y² 16 12 9 14 14. Factorize : 9 - (a² - 3a -1)² (a-1)(a+1)a+2 -a(a-4)(a+1)(a-1)(a-2) (a-4)(a-2)(a-1)(a+1) -(a-1)(a+1)a 15. When the polynomial x³ + mx² + 4x + 2 is divided by x + 2.What is the value of m? 4 5 3 2 16. Find the remainder when4x³+ 5x²- 4x+ 20 is divided by x+4 140 1 0 -140 17. If x4-kx3 + 10x² + lx - 3 is divisible by (x-1) and if when it is divided by (x+2) the remainder is 27, find the constants k and l, respectively. -15, -7 2, 3 8, -8 5, 7 18. Add the polynomials: (xy + 3x + 2) + (3x2 + y) 3x²+5xy+2 3x²+xy+3x+y+2 3x²+4xy+2 3x²+2xy+3x+2 19. Given that find the value of Q 2 1/2 1 1/3 20. If 9x² + 6xy + 4y² is a factor of 27x³ - 8y², find the other factor 4x-5y x+y 3x-2y x+3y 21. Given thatwhere A and B are constants, find the value of (A + B) 3 4 1 2 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 = 1/2 , b = 0, c = -3/2 and d = 1 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 23. Given that ax4 – 2x3 + cx2 – 6x – 9 = 0. When x = -1 or 3, calculate the values a and c, respectively. 1, 2 1, 0 2, -1 0, -1 24. Decompose into partial fractions : (5x2 + 12x + 3) / x(x + 1)2 2/(x+7) - 3/x²- 2/(x + 1)² 4/(x + 1)² +3/x x + 2/(x + 1) 3/x + 2/(x + 1) + 4/(x + 1)² 25. Simplify 2/5 1 2x-y 3/5 1 out of 25
