Question

For each polynomial function, rewrite the polynomial in standard form.

f(x) = (3x + 1)(x + 2)(x - 3)

Answer 1

To rewrite the polynomial f(x) in standard form, expand the product (3x + 1)(x + 2)(x - 3), then combine like terms to obtain 3x³ - 2x² - 19x - 6.

Step-by-step explanation:

To rewrite the polynomial f(x) = (3x + 1)(x + 2)(x - 3) in standard form, we need to expand the product of the three binomials.

1. Multiply the first two binomials: (3x + 1)(x + 2) gives 3x² + 6x + x + 2, which simplifies to 3x² + 7x + 2.
2. Now, multiply this trinomial by the last binomial: (3x² + 7x + 2)(x - 3).
3. Apply the distributive property (FOIL) to find the product: 3x³ - 9x² + 7x² - 21x + 2x - 6.
4. Combine like terms to get the polynomial in standard form: 3x³ - 2x² - 19x - 6.

The polynomial f(x) in standard form is 3x³ - 2x² - 19x - 6.