\( 2\left(10-2 x^{2}\right) \) Question 3(Multiple Choice Worth 2 points) (Factoring Algebraic Expressions MC) Rewrite \( \frac{1}{4} x^{3} y+\frac{3}{4} x y^{2} \) using a common factor. \( \frac{1}{4} x y\left(x^{2}+3 y\right) \) \( \frac{1}{4} x^{3} y^{2}(y+3 x) \) \( \frac{1}{2} x y\left(2 x^{2}+6 y\right) \) \( \frac{1}{2} x y\left(x^{2}+3 y\right) \)

Factor the expression by following steps: - step0: Factor: \(\frac{1}{4}x^{3}y+\frac{3}{4}xy^{2}\) - step1: Factor the expression: \(\frac{1}{4}\left(x^{3}y+3xy^{2}\right)\) - step2: Factor the expression: \(\frac{1}{4}xy\left(x^{2}+3y\right)\) To rewrite the expression \( \frac{1}{4} x^{3} y + \frac{3}{4} x y^{2} \) using a common factor, we can factor out the greatest common factor (GCF). 1. **Identify the GCF**: - The coefficients are \( \frac{1}{4} \) and \( \frac{3}{4} \). The GCF of these coefficients is \( \frac{1}{4} \). - The variable part has \( x^{3} y \) and \( x y^{2} \). The GCF for the variables is \( x y \). 2. **Factor out the GCF**: - Factoring out \( \frac{1}{4} x y \) from the expression gives: \[ \frac{1}{4} x y \left( x^{2} + 3 y \right) \] Thus, the expression can be rewritten as: \[ \frac{1}{4} x y \left( x^{2} + 3 y \right) \] Among the provided options, the correct answer is: \[ \frac{1}{4} x y \left( x^{2} + 3 y \right) \]