Write a polynomial f(x) that meets the given conditions. Answers

Write a polynomial f(x) that meets the given conditions. Answers may vary.
Degree 3 polynomial with zeros 5, 4, and -3
f(x)=
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macalpinee3
Step 1
Given:
The degree of polynomial is 3 and the zeros of polynomial are 5,4 and -3.
Step 2
The degree of the polynomial is the highest power is 3.
The zeros is a number where the value of polynomial becomes zero.
So,
$x=5⇒x-5=0$
$x=4⇒x-4=0$
$x=-3⇒x+3=0$
So,
f(x)=(x-5)(x-4)(x+3)=0
$f\left(x\right)=\left({x}^{2}-9x+20\right)\left(x+3\right)$
$f\left(x\right)={x}^{3}-9{x}^{2}+20x+3{x}^{2}-27x+60$
$f\left(x\right)={x}^{3}-6{x}^{2}-7x+60$
Hence,
$f\left(x\right)={x}^{3}-6{x}^{2}-7x+60$

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