Dividend = divisor x quotient + remainder－gpjqem1的部落格

標題:

Dividend = divisor x quotient + remainder

發問:

1.When the polynomial P(x) is divided by (x^2+2x-3), the remainder is (5x+2)P(x) = (x^2+2x-3) Q(x) + (5x+2)Find the remainder on dividing P(x) by (x-1)2.The remainder when polynomial P(x) is divided by (x-2) is 7 and the remainder when P(x) is divided by (x+3) is 2.Find the remainder when P(x) is... 顯示更多 1. When the polynomial P(x) is divided by (x^2+2x-3), the remainder is (5x+2) P(x) = (x^2+2x-3) Q(x) + (5x+2) Find the remainder on dividing P(x) by (x-1) 2. The remainder when polynomial P(x) is divided by (x-2) is 7 and the remainder when P(x) is divided by (x+3) is 2. Find the remainder when P(x) is divided by (x-2)(x+3).

最佳解答:

Q.1 P(x) = (x^2 +2x -3)Q(x) + 5x +2. = (x+3)(x-1)Q(x) + 5x +2 Put x=1 P(1) = 5 +2 = 7. Therefore, the remainder when divided by (x-1) is 7. Q.2 Let P(x) = (x-2)(x+3)Q(x) + ax + b. Put x=2 P(2) = 2a + b = 7 .....................(1) Put x = -3 P(-3) = -3a + b = 2 ................(2) (1)-(2) 5a = 5 therefore, a = 1, so b= 5. Therefore, the remainder when P(x) is divided by (x-2)(x+3) is x +5.