fultorise \( 5 a^{2}-23 a+12 \)

It seems like you want to **factorize** the quadratic expression: \[ 5a^{2} - 23a + 12 \] Let's factorize it step by step. ### Step 1: Identify the Coefficients The quadratic expression is in the form: \[ ax^{2} + bx + c \] where: - \( a = 5 \) - \( b = -23 \) - \( c = 12 \) ### Step 2: Find Two Numbers That Multiply to \( a \times c \) and Add to \( b \) We need two numbers that: - Multiply to \( 5 \times 12 = 60 \) - Add up to \( -23 \) After examining the factors of 60, we find: \[ -3 \times -20 = 60 \quad \text{and} \quad -3 + (-20) = -23 \] ### Step 3: Rewrite the Middle Term Using These Numbers \[ 5a^{2} - 3a - 20a + 12 \] ### Step 4: Factor by Grouping Group the terms: \[ (5a^{2} - 3a) + (-20a + 12) \] Factor out the greatest common factor (GCF) from each group: \[ a(5a - 3) - 4(5a - 3) \] ### Step 5: Factor Out the Common Binomial Factor \[ (a - 4)(5a - 3) \] ### Final Factorized Form \[ 5a^{2} - 23a + 12 = (a - 4)(5a - 3) \]