Question

A given polynomial has a root of x = 3, an zero of x = -2, and an x-intercept of x = -1.The equation of this polynomial in factored form would be f(x) =The equation of this polynomial in standard form would be f(x) =

Polynomial factorization
ANSWERED
asked 2021-02-18

A given polynomial has a root of \(x = 3\), an zero of \(x = -2\), and an x-intercept of \(x = -1\).
The equation of this polynomial in factored form would be \(f(x) =\)
The equation of this polynomial in standard form would be \(f(x) =\)

Answers (1)

2021-02-20

Step 1
Zeros, roots, and x-intercepts are all names for values that make a function equal to zero.
Given, a polynomial, f(x), has a root of \(x = 3\), a zero of \(x = -2\), and an x-intercept of \(x = -1\).
Step 2
1. The equation of this polynomial in factored form would be :
\(f(x) = (x-3)(x-(-2))(x-(-1))\)
\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}+{2}\right)}{\left({x}+{1}\right)}\)
2. The equation of this polynomial in standard form would be :
\(\displaystyle{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}^{{{2}}}+{3}{x}+{2}\right)}\)
\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}+{3}{x}^{{{2}}}+{2}{x}-{3}{x}^{{{2}}}-{9}{x}-{6}\)
\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}-{7}{x}-{6}\)

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