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)

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

1. Simplify the \( x^2 \) terms:
   \[
   4x^2 - 3x^2 = x^2
   \]
   So, the expression simplifies to:
   \[
   x^2 + 5x - 24
   \]

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

**Option 1: \( 4x(x - 6) \)**
   \[
   4x(x - 6) = 4x^2 - 24x
   \]
   This does not match \( x^2 + 5x - 24 \).

**Option 2: \( (x + 8)(x - 3) \)**
   \[
   (x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24
   \]
   This matches the expression \( x^2 + 5x - 24 \).

**Option 3: \( 2(x - 12) \)**
   \[
   2(x - 12) = 2x - 24
   \]
   This does not match \( x^2 + 5x - 24 \).

**Option 4: \( (x + 6)(x - 4) \)**
   \[
   (x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24
   \]
   This does not match \( x^2 + 5x - 24 \).

The correct answer is:

**\( (x + 8)(x - 3) \)**

Do you want more details or have any questions?

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

Explore how to simplify and identify equivalent expressions problem involving algebraic manipulation. The solution involves polynomial simplification and matching expressions, suitable for Grades 7-9.

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