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)=x2+7xg(x)=x−8
Step 2: Multiply the Functions
Next, we multiply f(x) and g(x):
f(x)⋅g(x)=(x2+7x)⋅(x−8)
Step 3: Expand the Product
We expand the product using the distributive property:
(x2+7x)⋅(x−8)=x2⋅x+x2⋅(−8)+7x⋅x+7x⋅(−8)=x3−8x2+7x2−56x
Step 4: Simplify the Expression
Combine like terms to simplify the expression:
x3−8x2+7x2−56x=x3−x2−56x