QuestionConsider the following polynomial. $h(x)=-8 x^{2}(x+9)(x-1)$
Step 1 of 2: Find the degree and leading coefficient of $\mathrm{h}(\mathrm{x})$ .

Studdy Solution

STEP 1

1. The polynomial is given in factored form as $h(x) = -8x^2(x+9)(x-1)$ .
2. The degree of a polynomial is the sum of the exponents of the variable $x$ in its expanded form.
3. The leading coefficient is the coefficient of the term with the highest degree when the polynomial is expanded.

STEP 2

1. Determine the degree of the polynomial.
2. Determine the leading coefficient of the polynomial.

STEP 3

To find the degree of the polynomial, we need to sum the exponents of $x$ from each factor:
- The factor $-8x^2$ contributes a degree of 2. - The factor $(x+9)$ contributes a degree of 1. - The factor $(x-1)$ contributes a degree of 1.
Therefore, the degree of the polynomial is:
$2 + 1 + 1 = 4$

STEP 4

To find the leading coefficient, consider the coefficient of the term with the highest degree when the polynomial is expanded:
- The coefficient from $-8x^2$ is $-8$ . - The highest degree term will be formed by multiplying the highest degree terms from each factor: $x^2$ from $-8x^2$ , $x$ from $(x+9)$ , and $x$ from $(x-1)$ .
Thus, the leading coefficient is:
$-8 \times 1 \times 1 = -8$
The degree of the polynomial is $\boxed{4}$ and the leading coefficient is $\boxed{-8}$ .

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