Question

Express your answer as a polynomial in standard form.

f(x) = x² – 7x + 5
g(x) = -x + 2
Find: (f•g)(x)

Answer 1

The product (f•g)(x) of the given functions f(x) = x² – 7x + 5 and g(x) = -x + 2 is found by multiplying the terms of the functions together. The result in standard form is -x³ + 9x² - 19x + 10.

Step-by-step explanation:

The student has asked how to find the product of two functions, f(x) and g(x), and express it as a polynomial in standard form. The given functions are f(x) = x² – 7x + 5 and g(x) = -x + 2. To find the product (f•g)(x), we multiply each term of f(x) by each term of g(x).

Multiplying f(x) by g(x) gives us:

1. x² * (-x) = -x³
2. x² * 2 = 2x²
3. (-7x) * (-x) = 7x²
4. (-7x) * 2 = -14x
5. 5 * (-x) = -5x
6. 5 * 2 = 10

Now, combine like terms to write the polynomial in standard form:

(f•g)(x) = -x³ + (2x² + 7x²) + (-14x - 5x) + 10

(f•g)(x) = -x³ + 9x² - 19x + 10

So, the product of the functions, (f•g)(x), when expressed in standard form, is -x³ + 9x² - 19x + 10.