Respuesta :
Answer:
The zeros of the given polynomial function f(x) are -3,0,-4
Step-by-step explanation:
Given polynomial is [tex]f(x)=3x^3+21x^2+36x[/tex]
To find the zeros of the given polynomial:
First equate the polynomial function f(x) to zero
That is [tex]f(x)=3x^3+21x^2+36x=0[/tex]
By synthetic division we can solve it
-3_| 3 21 36 0
0 -9 -36 0
_____________________
3 12 0 0
Therefore x+3 is a factor
That is x=-3 is a zero
[tex]3x^2+12x=0[/tex]
[tex]3x(x+4)=0[/tex]
3x=0 or x+4=0
Therefore x=0 or x=-4
Therefore the zeros are -3,0,-4
The zeros of the given polynomial function f(x) are -3,0,-4
Given polynomial is
[tex]f(x)=3x^3+21x^2+36x[/tex]
We have to find the zeros of the given polynomial
First equate the polynomial function f(x) to zero
[tex]f(x)=3x^3+21x^2+36x[/tex]
What is the synthetic division?
Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor
By synthetic division, we can solve it
-3_| 3 21 36 0
0 -9 -36 0
_____________________
3 12 0 0
Therefore x+3 is a factor
That is x=-3 is a zero
[tex]3x^2+12x=0[/tex]
[tex]3x(x+4)=0[/tex]
3x=0 or x+4=0
Therefore x=0 or x=-4
Therefore the zeros are -3,0,-4.
To learn more about the zeros visit:
https://brainly.com/question/20896994
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