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

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 $f(x) \cdot g(x)=x^{3}-x^{2}-56 x$
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Solution

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Solution Steps

To solve this problem, we need to find the product of the functions f(x) f(x) and g(x) g(x) . First, we will express f(x) f(x) and g(x) 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)=x2+7x f(x) = x^2 + 7x g(x)=x8 g(x) = x - 8

Step 2: Multiply the Functions

Next, we multiply f(x) f(x) and g(x) g(x) : f(x)g(x)=(x2+7x)(x8) f(x) \cdot g(x) = (x^2 + 7x) \cdot (x - 8)

Step 3: Expand the Product

We expand the product using the distributive property: (x2+7x)(x8)=x2x+x2(8)+7xx+7x(8) (x^2 + 7x) \cdot (x - 8) = x^2 \cdot x + x^2 \cdot (-8) + 7x \cdot x + 7x \cdot (-8) =x38x2+7x256x = x^3 - 8x^2 + 7x^2 - 56x

Step 4: Simplify the Expression

Combine like terms to simplify the expression: x38x2+7x256x=x3x256x x^3 - 8x^2 + 7x^2 - 56x = x^3 - x^2 - 56x

Final Answer

f(x)g(x)=x3x256x\boxed{f(x) \cdot g(x) = x^3 - x^2 - 56x}

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