質問: f4 maths dividing polynomials6 1. divide the following polynomial.find q(x),r(x) no need the steps. (x^4+2x^3-12x^2-4) / (x^2-2x-6) 2. when a is divided by x^2+x+1, the q(x) is x^2-2 with r(x) 2x+7. find the q(x) and r(x) when a is divided by x^2-2x+4.
回答: 1. divide the following polynomial. find q(x), r(x) no need the steps. (x^4+2x^3-12x^2-4) / (x^2-2x-6) 1+4+2 ------------------------ 1-2-6 ) 1+2-12+0-4 1-2-6 -------------- 4-6+0 4-8-24 ----------------- 2+24-4 2 - 4-12 --------------- 28+8 q(x) = x^2 + 4x + 2 r(x) = 28x + 8 2. when a is divided by x^2+x+1, the q(x) is x^2-2 with r(x) 2x+7. find the q(x) and r(x) when a is divided by x^2-2x+4. a = (x^2+x+1) q(x) + r(x) = (x^2+x+1)(x^2-2)+2x+7 = x^4+x^3-x^2-2x-2+2x+7 = x^4+x^3-x^2+5 1+3+1 ------------------ 1-2+4 ) 1+1-1+0+5 1-2+4 -------------- 3-5+0 3-6+12 ----------------- 1-12+5 1 - 2+4 ----------------- -10+1 q(x) = x^2 + 3x + 1 r(x) = -10x + 1