# Find an equation of a degree 3 polynomial(in factor form)

Find an equation of a degree 3 polynomial(in factor form) with the given zeros of f(x): -5,2,3. Assume the leading coefficient is 1.
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lalilulelo2k3eq
Step 1
given, A degree 3 polynomial with the given zeros of f(x) :−5,2,3 leading coefficient is 1.
Step 2
Now,
So, zeros of f(x): -5,2,3
$\therefore x=-5$
(x+5) is a factor.
$\therefore x=2$
(x-2) is a factor.
$\therefore x=3$
(x-3) is a factor.
Step 3
$\therefore$ The polynomial f(x) becomes
f(x)=(x+5)(x-2)(x-3)
$=\left(x+5\right)\left({x}^{2}-5x+6\right)$
$=x\left({x}^{2}-5x+6\right)+5\left({x}^{2}-5x+6\right)$
$={x}^{3}-5{x}^{2}+6x+5{x}^{2}-25x+30$
$={x}^{3}-19x+30$
$\therefore f\left(x\right)={x}^{3}-19x+30$