Determine the resulting polynomial: f(x)=8x+9 g(x)=-7x^2+5x-1 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:
$$f(x) = 8x + 9$$
$$g(x) = -7x^2 + 5x - 1$$

We will use the distributive property to multiply each term in $f(x)$ by each term in $g(x)$:

$$f(x) \cdot g(x) = (8x + 9) \cdot (-7x^2 + 5x - 1)$$

Now, distribute $8x$ and $9$ across the terms in $g(x)$:

$$= 8x \cdot (-7x^2) + 8x \cdot (5x) + 8x \cdot (-1) + 9 \cdot (-7x^2) + 9 \cdot (5x) + 9 \cdot (-1)$$

Calculate each term:

$$= -56x^3 + 40x^2 - 8x - 63x^2 + 45x - 9$$

Combine like terms:

$$= -56x^3 + (40x^2 - 63x^2) + (-8x + 45x) - 9$$

$$= -56x^3 - 23x^2 + 37x - 9$$

So, the resulting polynomial is:

$$f(x) \cdot g(x) = -56x^3 - 23x^2 + 37x - 9$$