3) \( 3 n^{2}-8 n+4 \)

To factor the quadratic expression \( 3n^{2} - 8n + 4 \), you can follow these steps: ### Step 1: Identify the Coefficients The given quadratic is in the form \( an^{2} + bn + c \), where: - \( a = 3 \) - \( b = -8 \) - \( c = 4 \) ### Step 2: Find Two Numbers That Multiply to \( a \times c \) and Add to \( b \) We need two numbers that multiply to \( 3 \times 4 = 12 \) and add up to \( -8 \). - The numbers are **-6** and **-2** because: - \( (-6) \times (-2) = 12 \) - \( (-6) + (-2) = -8 \) ### Step 3: Rewrite the Middle Term Using These Numbers Rewrite the expression by splitting the middle term using the numbers found: \[ 3n^{2} - 6n - 2n + 4 \] ### Step 4: Factor by Grouping Group the terms in pairs and factor out the common factors: \[ = (3n^{2} - 6n) + (-2n + 4) \\ = 3n(n - 2) - 2(n - 2) \] ### Step 5: Factor Out the Common Binomial Now, factor out the common binomial \((n - 2)\): \[ = (3n - 2)(n - 2) \] ### Final Factored Form \[ 3n^{2} - 8n + 4 = (3n - 2)(n - 2) \] **Therefore, the factored form of \( 3n^{2} - 8n + 4 \) is \((3n - 2)(n - 2)\).**