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

kloseyq 2021-12-15 Answered
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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Expert Answer

lalilulelo2k3eq
Answered 2021-12-16 Author has 38 answers
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
x=5
(x+5) is a factor.
x=2
(x-2) is a factor.
x=3
(x-3) is a factor.
Step 3
The polynomial f(x) becomes
f(x)=(x+5)(x-2)(x-3)
=(x+5)(x25x+6)
=x(x25x+6)+5(x25x+6)
=x35x2+6x+5x225x+30
=x319x+30
f(x)=x319x+30
with leading coefficient of 1.
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