To find the zeros of the polynomial, we set the polynomial equal to zero and solve for x:
x - x^2 - x^6 + 8x^4 = 0
Factoring out an x^2 from the last two terms gives us:
x(x^5 - x + 8x^2) = 0
Setting each factor equal to zero gives us two possibilities:
x = 0
x^5 - x + 8x^2 = 0
Let's solve the second equation:
Using synthetic division, we can divide x^5 - x + 8x^2 by x - 1 to get:
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1 | 1 0 -1 0 8 0
| 1 1 0 0 8
|______________________
1 1 0 0 8
The remainder is 8, so x - 1 is not a factor of x^5 - x + 8x^2.
Therefore, the only zero of the polynomial x - x^2 - x^6 + 8x^4 is x = 0.
Identify the number of zeros of the polynomial.
x - x^2 - x^6 + 8x^4
1 answer
1 answer