Question
POSSIBLE POINTS: 3.38
Factor the polynomial to find its zeros.
. Enter exact (no decimals) answers from least to greatest separated by a comma with
no spaces.
Factor the polynomial to find its zeros.
no spaces.
Ask by Elliott Coles. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The zeros are -√6, 1/2, and √6.
Solution

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The Deep Dive
To find the zeros of the polynomial
, we first look for rational roots using the Rational Root Theorem. Testing potential roots, we find that
is a root. We can then perform synthetic division of
by
to simplify the polynomial:
Thus,
.
Next, we can factor the quadratic
using the method of factoring or the quadratic formula. It factors as:
So, the complete factorization of the polynomial is:
Setting each factor equal to zero gives us the zeros:
-
→ -
→ -
→
Now, writing the zeros in order from least to greatest, we have:
Thus, the final answer is:
-2,\frac{3}{2},1