# 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) =

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 $f\left(x\right)=$
The equation of this polynomial in standard form would be $f\left(x\right)=$

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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 :
$f\left(x\right)=\left(x-3\right)\left(x-\left(-2\right)\right)\left(x-\left(-1\right)\right)$
$⇒f\left(x\right)=\left(x-3\right)\left(x+2\right)\left(x+1\right)$
2. The equation of this polynomial in standard form would be :
$f\left(x\right)=\left(x-3\right)\left({x}^{2}+3x+2\right)$
$⇒f\left(x\right)={x}^{3}+3{x}^{2}+2x-3{x}^{2}-9x-6$
$⇒f\left(x\right)={x}^{3}-7x-6$