Let f(x) =2x^3-5x^2-7x+3.
a)Find the remainder when f(x) is divided by
(i)x-3;
(ii)x+1.
b)If Ax+B is the remainder when f(x) is divided by (x-3)(x+1) , find, without actual division, the values of A and B.
Ans: (a)(i) -9 (ii)3 (b)A= -3, B=0
Formulae and Polynomials
2007-06-19 9:07 pm
回答 (1)
2007-06-19 9:16 pm
✔ 最佳答案
ai)f(3) = 54 - 45 - 21 + 3 = -9
ii)
f(-1) = -2-5+7+3 = 3
b)
f(x) = Q(x)(x-3)(x+1) + Ax+B
f(3) = 3A + B = -9 ----- (1)
f(-1) = -A + B = 3 ------- (2)
(1) - (2), 4A = -12, A = -3 ---- (3)
sub (3) into (2), B = 0
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