Welcome to your Algebra II(Senior Class Math Study by Topics ) NAME EMAIL PHONE NUMBER 1. Use Bionomial Theorem to find the first three terms in the expansion of (1 + x)15 2 + 45x + 735x² 3x+ 536x³ 1 + 15x + 105x² 45 + 46x² +342x³ 2. Factorize the polynomial x 3 - 1 (x - 1)(x² + x + 1) x-1 2x+1 (x-1)² 3. Factorize : (4x+3)² - (3x-2)² x(7x+1) (x-5)(7x-1) (x+5)(7x+1) (x+1)(x+5) 4. Find the coefficient of x³ in the binomial expansion of (2-5x)7 12000 -70000 50000 -30000 5. Find the second term in the expansion of (2+3x)12 4096 334 22x² 73728x 6. 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 7. If x= 2 is a root of the equation 2x³-2x²-5x+2 find the other roots 1.7433 3.446 0.566 0.366 8. Find the remainder when 12x4-9x2-2x-1 is divided by 2x+1 1/x x-1 1+x 0 9. Find the binomial expansion of (0.7)5 5.8589 0.16807 108.67 45.075 10. Find the third term in the binomial expansion of (2-a)10 11520a² 45332a² 45332a 11520a 11. 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 = -1 / 7, b = 1, c = 1, d = 0, e = -4 a = 8, b = 0, c = 1, d = 10, e = 2 a = -1 / 8, b = 0, c = 1, d = 0, e = -2 a = -18, b =4, c = 14, d = 0, e = -2 12. Subtract the polynomials: (-x2 + 5 x) - (6 x2 + x - 2) 5x²+6x -7x²+4x+2 -5x²+6x+2 5x²+6x-2 13. If (1 + 4x)5 = 1 + Ax + Bx² + Cx³... find the values of the constants, A, B and C, respectively 63, 783, 363 300, 45, 63 20, 160, 640 245, 647, 63 14. Subtract the polynomials: (9 x - 6) - (- 5x + 7) -4x - 13 -4x + 13 4x + 1 14x - 13 15. Use binomial theorem to expand (1 - 4x)³ in ascending powers of x 1 - 12x + 64x3 1 - 12x + 48x2 + 64x3 1 - 2x + 8x2 + 14x3 1 - 12x + 48x2 16. Subtract the polynomials: (xy + 3x + 2) - (3x2 + y) 3x²+4xy+2 -3x²+3x-y+2 -3x²+xy+3x-y+2 17. Factorize the polynomial (x + 1) 2 - 4 (x²- 1)(x + 3) (x - 1)(x² + 3) (x² - 1)(x² + 3) (x - 1)(x + 3) 18. Given that ax4 – 2x3 + cx2 – 6x – 9 = 0. When x = -1 or 3, calculate the values a and c, respectively. 1, 2 1, 0 0, -1 2, -1 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 + 10x3 + 5x4 + x5, 1.6105 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.6105 1 + 5x + 10x2 + x5, 1.610534 1 + 5x + 10x2 + 10x3 + 5x4 + x5, 1.61 20. If find P + Q + R. 4 2 3 1 21. If (1 + px)n = 1 + 2x - 3x² + ... where Px<1, determine the values of p and n, respectively. 3/4, 7 7, 3/4 5, 2/5 2/5, 5 22. Subtract the polynomials: (x2y + 3x + 2) - (2 + xy2 + 3x) x²y-xy² 0 x²y+xy² -2x²y 23. If the function f(x) = x³ + 2x² +qx - 6 is divisible by x + 1, find q -5 -2 5 1 24. Find the roots of x³ + 2x² - 5x + 6 = 0 1, 3, 2 -1, 3 1, -2, -3 -1, -3, 2 25. Find a positive value of p if the expression 2x² - px - + p leaves a remainder 6 when divided by x-p 2 4 3 5 1 out of 25
