Question

A polynomial function f is defined as f(x)=3(5x+3)(x+2)(7x-1). Which of the

Answer 1

The polynomial function
`\( f(x) = 3(5x + 3)(x + 2)(7x - 1) \)` can be expanded to
`\( f(x) = 105x^3 + 157x^2 - 89x - 18 \).`

Step-by-step explanation:

To find the expanded form of the polynomial function, we apply the distributive property by multiplying each term within the parentheses. For the given function
`\( f(x) = 3(5x + 3)(x + 2)(7x - 1) \),` we multiply the terms inside the first set of parentheses, then multiply the result by the terms inside the second set of parentheses, and finally multiply the new result by the terms inside the third set of parentheses.

Starting with
`\( 3(5x + 3) \)`, we get
`\( 15x + 9 \).` Then, multiplying this by
`\( (x + 2) \),` we get
`\( (15x + 9)(x + 2) = 15x^2 + 39x + 18 \).` Multiplying this by
`\( (7x - 1) \),` we get
`\( 105x^3 + 157x^2 - 89x - 18 \).`

Therefore, the expanded form of the given polynomial function is
`\( f(x) = 105x^3 + 157x^2 - 89x - 18 \).`

In summary, the expression
`\( 3(5x + 3)(x + 2)(7x - 1) \)` simplifies to
`\( 105x^3 + 157x^2 - 89x - 18 \)`, providing a clear representation of the polynomial in standard form.

Complete Question:

A polynomial function f is defined as f(x)=3(5x+3)(x+2)(7x-1). Which of the can be expanded?