let f(x)=kx3次-5x2次-22x2-15,where k is a constant. it is known that x-5 is a factor of f(x).
a. find k
b factorize f(x+2)
中4 f(x)數學問題
2010-07-10 10:25 pm
回答 (2)
2010-07-10 10:45 pm
✔ 最佳答案
a)f(x) = kx^3 - 5x^2 - 22x - 15
By remainder theoream ,
f(5) = k(5)^3 - 5(5^2) - 22(5) - 15 = 0
125k - 125 - 125 = 0
k = 2
b) Firstly , factorize
f(x) = 2x^3 - 5x^2 - 22x - 15
= (x - 5)(2x^2 + 5x + 3)
= (x - 5)(x + 1)(2x + 3)
So
f(x+2)
= (x+2 - 5)(x+2 + 1)(2(x+2) + 3)
= (x - 3)(x + 3)(2x + 7)
2010-07-16 9:04 pm
答得好!!!!!!!!!!!!!!!!!!!!!!!
收錄日期: 2021-04-21 22:16:39
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