Answer
Please see "step by step"
Work Step by Step
(see page 384)
For estimating the possible number of NEGATIVE zeros,
we start with the defining expression of the polynomial,
$f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{2}x^{2}+a_{1}x+a_{0}$
where the coefficients are real numbers.
Then, we substitute $x$ with $-x$ and express $f(-x).$
What will happen is that all terms with odd exponents will change signs, and the evens will remain the same as in $f(x).$
We then count the number of sign changes in the expression for $f(-x):$
The number of NEGATIVE real zeros of $f$ is either
$\mathrm{a}$. the same as the number of sign changes of $f(-x)$
or
$\mathrm{b}$. less than the number of sign changes of $f(-x)$ by a positive even integer.
If $f(-x)$ has only one variation in sign, then $f$ has exactly one negative real zero.
