Question

find a and b if x^5-x^4+4x^3+3x^2+3x+b if x^3+2x^2+a is a factor

Answer 1

$( {x}^{5} - {x}^{4} + 4 {x}^{3} + 3 {x}^{2} + 3x + b) \div ( {x}^{3} + 2 {x}^{2} + a \\ q = {x}^{2} - 3x + 10 \\ r = ( - a - 17) {x}^{2} + (3 + 3a)x + b - 10a \\ hence \\ - a - 17 = 0 \: \: \: \: or \: \: \: \: 3 + 3a = 0 \\a = - 17 \: \: \: \: \: \: \: or \: \: \: \: \: a = - 1 \\ b - 10a = 0 \\ b = - 170\: \: \: \: \: \: or \: \: \: \: b = - 10$