Question

which expression is equivalent to $24x^2 - 22x + 5$?
a $(12x + 5)(2x + 1)$
b $(8x - 5)(3x - 1)$
c $(12x - 5)(2x - 1)$
d $(8x + 5)(3x + 1)$

1. text

enter question

Explanation:

Step1: Expand Option A

Multiply \((12x + 5)(2x + 1)\) using the distributive property (FOIL method):
\(12x \cdot 2x + 12x \cdot 1 + 5 \cdot 2x + 5 \cdot 1 = 24x^2 + 12x + 10x + 5 = 24x^2 + 22x + 5\).
This does not match \(24x^2 - 22x + 5\), so A is incorrect.

Step2: Expand Option B

Multiply \((8x - 5)(3x - 1)\):
\(8x \cdot 3x + 8x \cdot (-1) + (-5) \cdot 3x + (-5) \cdot (-1) = 24x^2 - 8x - 15x + 5 = 24x^2 - 23x + 5\).
This does not match, so B is incorrect.

Step3: Expand Option C

Multiply \((12x - 5)(2x - 1)\):
\(12x \cdot 2x + 12x \cdot (-1) + (-5) \cdot 2x + (-5) \cdot (-1) = 24x^2 - 12x - 10x + 5 = 24x^2 - 22x + 5\).
This matches the given expression, so we can confirm C is correct (optional: check D for completeness).

Step4: Expand Option D (Optional)

Multiply \((8x + 5)(3x + 1)\):
\(8x \cdot 3x + 8x \cdot 1 + 5 \cdot 3x + 5 \cdot 1 = 24x^2 + 8x + 15x + 5 = 24x^2 + 23x + 5\).
This does not match, so D is incorrect.

Answer:

C. \((12x - 5)(2x - 1)\)