Question

part c
question
what are the factors of the equation representing jared’s function?
□ (x + 9)
☑ (x - 10)
□ (x + 3)
☑ (x - 9)
□ (x + 10)
☑ (x - 3)
part d
question
use the factors of the function and the y-intercept to find the standard form of the equation representing jared’s function.
type the correct answer in the box.
f(x) =
there is a virtual keyboard on the left side of the input box, including numbers, operation symbols, trigonometric functions, logarithms, etc.

Explanation:

Step1: Multiply the selected factors

First, expand the product of the chosen factors: $(x-3)(x-9)(x-10)$
First multiply $(x-3)(x-9)$:

$$\begin{align*} (x-3)(x-9) &= x^2 -9x -3x +27 \\ &= x^2 -12x +27 \end{align*}$$

Step2: Multiply by the third factor

Now multiply the result by $(x-10)$:

$$\begin{align*} (x^2 -12x +27)(x-10) &= x^3 -10x^2 -12x^2 +120x +27x -270 \\ &= x^3 -22x^2 +147x -270 \end{align*}$$

This is the standard form, and the y-intercept is $-270$, which matches the constant term.

Answer:

$f(x)=x^3 -22x^2 +147x -270$