## Factoring and Finding Roots of (x+2)(x-1)(x-4)

The expression (x+2)(x-1)(x-4) is already in factored form. This makes it easy to find the roots (or zeros) of the expression.

### Understanding Factored Form

In factored form, each factor represents a linear expression that equals zero when the variable (x) takes on a specific value. This value is called the root or zero.

### Finding the Roots

To find the roots, we set each factor equal to zero and solve for x:

**x + 2 = 0**- Subtract 2 from both sides: x = -2

**x - 1 = 0**- Add 1 to both sides: x = 1

**x - 4 = 0**- Add 4 to both sides: x = 4

Therefore, the roots of the expression (x+2)(x-1)(x-4) are **x = -2, x = 1, and x = 4**.

### Expanding the Expression

We can expand the expression to get a polynomial form:

**Expand the first two factors:**- (x + 2)(x - 1) = x² + x - 2

**Multiply the result by the third factor:**- (x² + x - 2)(x - 4) = x³ - 3x² - 6x + 8

So, the expanded form of the expression is **x³ - 3x² - 6x + 8**.

### Summary

**Factored Form:**(x+2)(x-1)(x-4)**Roots:**x = -2, x = 1, x = 4**Expanded Form:**x³ - 3x² - 6x + 8

Understanding factored form is crucial in solving equations, graphing functions, and analyzing the behavior of polynomials.