To find all the zeros of the polynomial [tex]\( f(x) = x^4 + 16x^3 + 47x^2 - 100x - 132 \)[/tex], we will follow the procedure to determine the roots of the polynomial equation [tex]\( f(x) = 0 \)[/tex].
Step-by-Step Solution:
1. Identify the Polynomial:
The given polynomial is [tex]\( f(x) = x^4 + 16x^3 + 47x^2 - 100x - 132 \)[/tex].
2. Determine the Roots:
To find the roots of the polynomial, we solve the equation [tex]\( f(x) = 0 \)[/tex].
3. Verify and List the Roots:
After solving, we find the roots of the polynomial to be:
[tex]\[
-11, -6, -1, 2
\][/tex]
4. Arrange the Roots in Ascending Order:
The roots should be arranged from smallest to largest. Considering the roots we have:
[tex]\[
-11, -6, -1, 2
\][/tex]
Therefore, the zeros of the polynomial [tex]\( f(x) = x^4 + 16x^3 + 47x^2 - 100x - 132 \)[/tex] arranged from smallest to largest are:
[tex]\[
x = [-11, -6, -1, 2]
\][/tex]
