(x+2)(x-1)(x-4)

2 min read Jun 16, 2024
(x+2)(x-1)(x-4)

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:

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

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