Question

1. what is the degree of the polynomial product?2. enter the coefficients for each term in the product of $4x^2 + 9$ and $7x^2 - 8$. enter 0 as the coefficient of any terms not in the product.$\boldsymbol{(\quad)x^4+(\quad)x^3+(\quad)x^2+(\quad)x+(\quad)}$given filled parts: $(28)x^4+(0)x^3+(31)x^2+(\quad)x+(\quad)$

Explanation:

Step1: Expand the polynomial product

Use distributive property (FOIL for quadratics):
$$(4x^2 + 9)(7x^2 - 8) = 4x^2 \cdot 7x^2 + 4x^2 \cdot (-8) + 9 \cdot 7x^2 + 9 \cdot (-8)$$

Step2: Calculate each term

$$= 28x^4 - 32x^2 + 63x^2 - 72$$

Step3: Combine like terms

$$= 28x^4 + 0x^3 + (63-32)x^2 + 0x + (-72) = 28x^4 + 0x^3 + 31x^2 + 0x -72$$

Step4: Identify the degree

The degree is the highest exponent of $x$, which is 4.

Answer:

Degree of the polynomial product: 4
Completed polynomial coefficients:
$(28)x^4 + (0)x^3 + (31)x^2 + (0)x + (-72)$