Question

$-4x^{2}+2x-6$
what is the degree of the polynomial product?
enter the coefficients for each term in the product of $-4x^{2}+2x-6$ and $7x^{2}+4$.
enter 0 as the coefficient of any terms not in the product.
$\boldsymbol{( -28 )}x^{4}+\boldsymbol{( 14 )}x^{3}+\boldsymbol{( -58 )}x^{2}+(\quad)x+(\quad)$
options:
$2x$
$14x^{3}$
$8x$
$-6$
$-42x^{2}$
$-24$

Explanation:

Step1: Expand the polynomial product

$$(-4x^2 + 2x - 6)(7x^2 + 4)$$
$$= -4x^2(7x^2 + 4) + 2x(7x^2 + 4) -6(7x^2 + 4)$$

Step2: Distribute each term

$$= -28x^4 -16x^2 +14x^3 +8x -42x^2 -24$$

Step3: Combine like terms

$$= -28x^4 +14x^3 + (-16x^2-42x^2) +8x -24$$
$$= -28x^4 +14x^3 -58x^2 +8x -24$$

Step4: Identify missing coefficients

Match to the given polynomial form to find the remaining coefficients.

Answer:

The coefficient of $x$ is $\boldsymbol{8}$, and the constant term is $\boldsymbol{-24}$.
The completed polynomial is:
$$(-28)x^4 + (14)x^3 + (-58)x^2 + (8)x + (-24)$$