Determine the resulting polynomial: f(x)=2x+7 g(x)=-2x^2-8x+7 Find: f(x)cdot g(x) Answer Attemptiout of 2 square

To find the resulting polynomial $f(x) \cdot g(x)$, we need to multiply the two given polynomials $f(x)$ and $g(x)$.

Given:
$$f(x) = 2x + 7$$
$$g(x) = -2x^2 - 8x + 7$$

We will use the distributive property to multiply these polynomials:

$$f(x) \cdot g(x) = (2x + 7) \cdot (-2x^2 - 8x + 7)$$

Now, distribute each term in $f(x)$ to each term in $g(x)$:

$$= 2x \cdot (-2x^2) + 2x \cdot (-8x) + 2x \cdot 7 + 7 \cdot (-2x^2) + 7 \cdot (-8x) + 7 \cdot 7$$

Calculate each product:

$$= -4x^3 - 16x^2 + 14x - 14x^2 - 56x + 49$$

Combine like terms:

$$= -4x^3 - 30x^2 - 42x + 49$$

So, the resulting polynomial is:

$$f(x) \cdot g(x) = -4x^3 - 30x^2 - 42x + 49$$