(x^2-x+8)(x^2-2x-2)

Jasonbradley

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Jun 17, 2024

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Expanding the Expression (x^2 - x + 8)(x^2 - 2x - 2)

This article will explore the process of expanding the given expression and discuss the resulting polynomial.

Expanding the Expression

To expand the expression, we can utilize the distributive property. We will multiply each term in the first set of parentheses by each term in the second set of parentheses:

(x^2 - x + 8)(x^2 - 2x - 2)

Step 1: Expand x^2 from the first parentheses:

• x^2 * (x^2 - 2x - 2) = x^4 - 2x^3 - 2x^2

Step 2: Expand -x from the first parentheses:

• -x * (x^2 - 2x - 2) = -x^3 + 2x^2 + 2x

Step 3: Expand 8 from the first parentheses:

• 8 * (x^2 - 2x - 2) = 8x^2 - 16x - 16

Step 4: Combine all the terms:

• x^4 - 2x^3 - 2x^2 - x^3 + 2x^2 + 2x + 8x^2 - 16x - 16

Step 5: Simplify the expression by combining like terms:

• x^4 - 3x^3 + 8x^2 - 14x - 16

Resulting Polynomial

The expanded form of the expression (x^2 - x + 8)(x^2 - 2x - 2) is x^4 - 3x^3 + 8x^2 - 14x - 16.

This is a fourth-degree polynomial with the following characteristics:

• Leading Coefficient: 1
• Constant Term: -16
• Degree: 4

This polynomial can be used for various purposes, such as finding its roots, graphing its function, or analyzing its behavior.