Welcome to your Algebra II(Senior Class Math Study by Topics ) NAME EMAIL PHONE NUMBER 1. If y + 1/y = 4, find y² + 1/y² 9 14 16 12 2. Factorize : (4x+3)² - (3x-2)² (x+5)(7x+1) (x+1)(x+5) (x-5)(7x-1) x(7x+1) 3. Factorize the polynomial x 3 - x 2 - 25x + 25 (x - 1)(x + 5)(x - 5) (x - 1)(x + 5)² (x-5)² x²-1(x-5) 4. Decompose into partial fractions : (5x + 10) / x(x + 5) 2/x + 3/(x + 5) x/2 3/ (x+5) x/2 + 3/(x+3) 5. Find the third term in the binomial expansion of (2-a)10 45332a² 11520a² 45332a 11520a 6. What is the common factor to the binomial expressions 4x²-9y², 8x³+27y³ and (4x+6y)² 4x+6y 4x-6y 2x-3y 2x+3y 7. Find the binomial expansion of (2.01)6 34.573 65.944 12.322 24.544 8. Factorize : 9 - (a² - 3a -1)² (a-1)(a+1)a+2 (a-4)(a-2)(a-1)(a+1) -(a-1)(a+1)a -a(a-4)(a+1)(a-1)(a-2) 9. Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when divided by 2x + 1 -5 -10 4 10 10. What is the common factor to the expressions y²-y, 2y²+y-1 and y²-1? y+1 y y-1 None 11. Factorize the polynomial x 3 - 1 2x+1 (x-1)² (x - 1)(x² + x + 1) x-1 12. Simplify a/(a-3)(a-7) a/(a-3)(a+7) (a+3)(a+7)/a a/(a+3)(a+7) 13. Multiply x² + x + 1 by x² - x + 1 x4 - x² + 1 x4 -1 x4 + x² + 1 x3 + x- 1 14. Express in partial fractions 5/2(x+1) - 1/(x-1) 1/(x+1) + 4/(3-x) 5/2(x-1) - 1/2(x+1) x/(x+1) + 1/(x-1) 15. Use Bionomial Theorem to find the first three terms in the expansion of (1 + x)15 3x+ 536x³ 45 + 46x² +342x³ 1 + 15x + 105x² 2 + 45x + 735x² 16. Simplify 2(9+y) 81-y² -2(y-9) 2(y-9) 17. Use the binomial theorem to expand (1 + 2x)5 in ascending powers of x. Hence find the value of (1.02)5 correct to 4 decimal places. 1 + 10x + 40x² + 80x4 + 32x5, 1.1 1 + 10x + 40x² + 80x3 + 90x4 + 32x5, 1.10 1 + 10x + 40x² + 80x3 + 80x4 + 32x5, 1.1041 1 + 80x3 + 80x4 + 32x5, 1.1041 18. Factorize the polynomial (x + 1) 2 - 4 (x - 1)(x + 3) (x² - 1)(x² + 3) (x²- 1)(x + 3) (x - 1)(x² + 3) 19. 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 + x5, 1.610534 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.61 1 + 5x + 10x3 + 5x4 + x5, 1.6105 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.6105 20. Given that (1 + 3x)10 = 1 + Px +Qx² + Rx³...find the values of the integers P, Q and R, respectively. 98, 755, 8689 6, 54, 4754 30, 405, 3240 409, 67, 675 21. Find the binomial expansion of (1.04)5 1.5332 1.4633 2.4342 1.2167 22. Subtract the polynomials: (9 x - 6) - (- 5x + 7) 4x + 1 14x - 13 -4x - 13 -4x + 13 23. Divide the expression x³ + 7x² - x - 7 by -1+x² x²+2 x-7 x+7 x²-1 24. Given thatwhere A and B are constants, find the value of (A + B) 4 2 1 3 25. Find the second term in the expansion of (2+3x)12 73728x 334 4096 22x² 1 out of 25
