Math Problem Statement

Which of the following simplifies to the same expression as 4x2−3x2+5x−24

?(1 point)

Responses

4x(x−6)

4 x left parenthesis x minus 6 right parenthesis

(x+8)(x−3)

left parenthesis x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis

2(x−12)

2 left parenthesis x minus 12 right parenthesis

(x+6)(x−4)

Solution

The given expression is 4x23x2+5x244x^2 - 3x^2 + 5x - 24. Let's simplify this expression first:

  1. Simplify the x2x^2 terms: 4x23x2=x24x^2 - 3x^2 = x^2 So, the expression simplifies to: x2+5x24x^2 + 5x - 24

Now, we need to check which of the provided options simplifies to x2+5x24x^2 + 5x - 24.

Option 1: 4x(x6)4x(x - 6) 4x(x6)=4x224x4x(x - 6) = 4x^2 - 24x This does not match x2+5x24x^2 + 5x - 24.

Option 2: (x+8)(x3)(x + 8)(x - 3) (x+8)(x3)=x23x+8x24=x2+5x24(x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24 This matches the expression x2+5x24x^2 + 5x - 24.

Option 3: 2(x12)2(x - 12) 2(x12)=2x242(x - 12) = 2x - 24 This does not match x2+5x24x^2 + 5x - 24.

Option 4: (x+6)(x4)(x + 6)(x - 4) (x+6)(x4)=x24x+6x24=x2+2x24(x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24 This does not match x2+5x24x^2 + 5x - 24.

The correct answer is:

(x+8)(x3)(x + 8)(x - 3)

Do you want more details or have any questions?

Here are some related questions:

  1. How do you expand a binomial product?
  2. What is the process for factoring a quadratic expression?
  3. How do you simplify polynomial expressions?
  4. How can you verify if two expressions are equivalent?
  5. What are common techniques for factoring quadratics?
  6. How can errors occur when simplifying expressions?
  7. What are the steps to solve quadratic equations?
  8. What are the different forms of quadratic expressions?

Tip: Always simplify the expression first before comparing it to other options to identify the correct match.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Simplification
Quadratic Equations

Formulas

Quadratic equation formula ax^2 + bx + c = 0

Theorems

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Suitable Grade Level

Grades 7-9