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50000家学校 1000万学生的选择 美国高考（SAT）数学多项式函数考点实例     点击图片查看原图

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2019-06-26 15:47

31   您还没有登录，请登录后查看联系方式 发布bob体育竞技信息 推广bob体育竞技课程 建立学校主页 在线咨询课程   Recall that if K is a zero of a polynomial function defined as y=f(x), then x-k is a factor of f.

A polynomial function P has zeros -3,3/2,and 8. Which of the following polynomial functions could define P?

A. P(x)=-3(x-3/2)(x-8) B.P(x)=-(x-3)(x+3/2)(x+8) C. P(x)=(x+3)(3x-2)(x-8) D. P(x)=(x+3)(2x-3)(x-8)

Since the polynomial function P has the zeros -3,3/2,and 8,it follows that (x-(-3)),(x-3/2),and (x-8) must be factors of P.

Therefore, we can define P as P(x)=a(x+3)(x-3/2)(x-8), wher a is a nonzero constant.

A constant factor, such as a, does not affect the zeros of the polynomial function. In order to rewrite the equation with integral coeffecients, let a=2.

If a=2, it follows that

P(x)=a(x+3)(x-3/2)(x-8)

=2(x+3)(x-3/2)(x-8)

=(x+3)(2x-3)(x-8).

so the polynomial that could define P is P(x)=(x+3)(2x-3)(x-8).   ﻿