Questions: Let f(x)=x^2+7x and g(x)=x-8. Evaluate f(x) · g(x). A f(x) · g(x)=x^2-x-56 B f(x) · g(x)=x^3-15x^2-56x C f(x) · g(x)=x^2-x-15 D f(x) · g(x)=x^3-x^2-56x

Transcript text: Let $f(x)=x^{2}+7 x$ and $g(x)=x-8$. Evaluate $f(x) \cdot g(x)$. A $f(x) \cdot g(x)=x^{2}-x-56$ B $f(x) \cdot g(x)=x^{3}-15 x^{2}-56 x$ C $f(x) \cdot g(x)=x^{2}-x-15$ D $f(x) \cdot g(x)=x^{3}-x^{2}-56 x$

Solution

Solution Steps

To solve this problem, we need to find the product of the functions $ f(x) $ and $ g(x) $. First, we will express $ f(x) $ and $ g(x) $ in their given forms. Then, we will multiply these expressions together and simplify the resulting polynomial.

Step 1: Define the Functions

We start with the given functions: \[ f(x) = x^2 + 7x \] \[ g(x) = x - 8 \]

Step 2: Multiply the Functions

Next, we multiply $ f(x) $ and $ g(x) $: \[ f(x) \cdot g(x) = (x^2 + 7x) \cdot (x - 8) \]

Step 3: Expand the Product

We expand the product using the distributive property: \[ (x^2 + 7x) \cdot (x - 8) = x^2 \cdot x + x^2 \cdot (-8) + 7x \cdot x + 7x \cdot (-8) \] \[ = x^3 - 8x^2 + 7x^2 - 56x \]

Step 4: Simplify the Expression

Combine like terms to simplify the expression: \[ x^3 - 8x^2 + 7x^2 - 56x = x^3 - x^2 - 56x \]