I have the function:
f(x)=3x(x−3)^2(x+2)^3(x^2−3)
Would the degree be 7?
Please let me know if I am correct.
1+2+3+2 = 8
Thank you Damon for your help!
I saw the mistake I made.
Thanks again!
You are welcome :)
To determine the degree of a polynomial function, we need to find the highest power of the variable in the function.
In this case, we have the function f(x)=3x(x−3)^2(x+2)^3(x^2−3). Let's simplify this expression:
f(x) = 3x(x^2 - 6x + 9)(x + 2)^3(x^2 - 3)
Expanding the binomials and simplifying further:
f(x) = 3x(x^5 + 6x^4 + 4x^3 - 36x^2 - 48x - 144)(x^2 - 3)
Combining like terms and multiplying the remaining factors:
f(x) = 3x^7 + 3x^6 - 18x^5 - 108x^4 + 162x^3 + 972x^2 - 432x - 2592
The highest power of x in this function is x^7, which means the degree of the function is 7. Therefore, your answer is correct.