# Math Questions With Answers (9): Polynomial Division

More Math questions on synthetic division of polynomials are presented. Answers to these questions are located at the lower part of the page.

 Questions 1: Use synthetic division to find the quotient Q and remainder R when dividing the polynomial 2x2 + x by x - 1. Questions 2: Use synthetic division to find the quotient Q and remainder R when dividing the polynomial 4x3 + x2 - 2x + 3 by x + 2. Questions 3: Use synthetic division to find the quotient Q and remainder R when dividing the polynomial 7x5 - 2x4 - 5x3 + x2 - 3x + 5 by x - 2. Questions 4: Use synthetic division to find the quotient Q and remainder R when dividing the polynomial (1/2)x3 - (1/3)x2 - (3/2) x + 1/3 by x - 1/2. Questions 5: Use synthetic division to find the quotient Q and remainder R when dividing the polynomial 0.3 x3 - 0.2x2 - 0.1 x + 0.3 by x - 0.2. Questions 6: Use synthetic division and the remainder theorem to determine f(-2) given that f(x) = 5x4 - 4x3 - x2 + 5 Questions 7: Use synthetic division and the remainder theorem to determine f(1/2) given that f(x) = -3x5 + x3 - 2x2 + x - 3 Questions 8: Use synthetic division and the remainder theorem to determine f(0.2) given that f(x) = 0.1 x3 - 0.6x2 - 0.6 Questions 9: Use synthetic division to find the quotient Q and remainder R when dividing f(x) = x2 + 2x + 3 by x - i. (i = √(-1) the imaginary unit) Questions 10: Use synthetic division to find the quotient Q and remainder R when dividing f(x) = x5 + x4 + x3 +2x - 5 by x + i. (i = √(-1) the imaginary unit) ANSWERS TO ABOVE QUESTIONS 1) Q = 2x + 3 , R = 3 2) Q = 4x2 - 7x + 12 , R = -21 3) Q = 7x4 + 12x3 + 19x2 + 39x + 75, R = 155 4) Q = (1/2)x2 - (1/2)x - 37/24 , R = -7/16 5) 0.3 x2 - 0.14 x - 0.128 , R = 0.2744 6) 113 7) 95/32 8) -0.6232 9) Q = x + 2 + i , R = 2 + 2i 10) Q = x4 + (1 - i) x3 - ix2 - x + 2 + i , R = -2i - 4 More math questions and problems with detailed solutions in this site.