Question

Let f(x) = x2 − 2x + 2 and g(x) = x − 3. Find f(x) ⋅ g(x).

Answer 1

x³- 5x² + 8x - 6.

Explanation:

Given : f(x) = x2 − 2x + 2 and g(x) = x − 3.

To find : f(x) ⋅ g(x).

Solution : We have given

f(x) = x² − 2x + 2 and g(x) = x − 3.

We need to find the product

f(x) ⋅ g(x).

Plug the values of f(x) and g(x).

( x² − 2x + 2) ( x − 3).

Distribute x² over (x-3) and 2x over ( x − 3) and 2 over ( x − 3).

x²(x-3) - 2x ( x − 3)+ 2( x − 3).

x³-3x² -2x² + 6x + 2x - 6.

Combine like terms and solve

x³- 5x² + 8x - 6.

Therefore, x³- 5x² + 8x - 6.

Answer 2

x³ - 5x² + 8x - 6

Explanation:

f(x) × g(x)

= (x² - 2x + 2)(x - 3)

Each term in the first factor is multiplied by each term in the second factor, that is

x(x² - 2x + 2) - 3(x² - 2x + 2) ← distribute both parenthesis

= x³ - 2x² + 2x - 3x² + 6x - 6 ← collect like terms

= x³ - 5x² + 8x - 6