Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. -2, 1, 3

tricotasu

tricotasu

Answered question

2021-02-19

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. -2, 1, 3

Answer & Explanation

hosentak

hosentak

Skilled2021-02-20Added 100 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)(x−1)(x−3)
Expand:
f(x)=a(x2+x2)(x3)
f(x)=a[x(x2+x2)3(x2+x2)]
f(x)=a(x3+x22x3x23x+6)
f(x)=a(x32x25x+6)
Since the leading coefficient is 1, we let a=1:
f(x)=x32x25x+6
Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

Answer is given below (on video)

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