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

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 $$f(x) =$$

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 :
$$\displaystyle{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}^{{{2}}}+{3}{x}+{2}\right)}$$
$$\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}+{3}{x}^{{{2}}}+{2}{x}-{3}{x}^{{{2}}}-{9}{x}-{6}$$
$$\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}-{7}{x}-{6}$$