Write a polynomial function $f$ of least degree that has rational coefficients, a leading coefficient of 1, and the given zero(s). $-2,\ 3,\ 6$

Answered question

2021-12-09

Write a polynomial function $f$f​ of least degree that has rational coefficients, a leading coefficient of 1, and the given zero(s).

$-2,\ 3,\ 6$

Answer & Explanation

Vasquez

Vasquez

Expert2022-02-21Added 669 answers

If a is a zero of a polynomial, then x−a is one of its factors. Given the zeros -2, 1, and 3, we write:
f(x)=a(x+2)(x2)(x6)

Expand the following:
f(x)=(x+2)(x2)(x6)

Multiply x - 2 and x - 6 together using FOIL.
(x2)(x6)

=(x)(x)+(x)(6)+(2)(x)+(2)(6)

=x26x2x+12

=x28x+12:
f(x)=(x28x+12)(x+2)

Multiply out (x+2)(x28x+12).

f(x)=(x36x24x+24)
Answer:  
f(x)=(x36x24x+24)

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