Ask AI: factor 5x²-18x+9

To factor the quadratic expression \(5x² - 18x + 9\), follow these steps: 1. **Identify the coefficients**: The quadratic expression is in the form \(ax² + bx + c\), where \(a = 5\), \(b = -18\), and \(c = 9\). 2. **Multiply \(a\) and \(c\)**: \( a \times c = 5 \times 9 = 45 \). 3. **Find two numbers that multiply to \(ac\) and add up to \(b\)**: We need to find two numbers whose product is 45 and whose sum is -18. These numbers are -3 and -15 because: \( -3 \times -15 = 45 \) \( -3 + (-15) = -18 \). 4. **Rewrite the middle term (\(bx\)) using these two numbers**: Rewrite \(-18x\) as \(-3x - 15x\): \[ 5x² - 3x - 15x + 9 \] 5. **Group the terms in pairs**: \[ (5x² - 3x) + (-15x + 9) \] 6. **Factor out the greatest common factor (GCF) from each pair**: From \(5x² - 3x\), factor out \(x\): \[ x(5x - 3) \] From \(-15x + 9\), factor out \(-3\): \[ -3(5x - 3) \] 7. **Factor by grouping**: Now the expression looks like this: \[ x(5x - 3) - 3(5x - 3) \] Notice that \((5x - 3)\) is a common factor: \[ (5x - 3)(x - 3) \] Therefore, the factored form of \(5x² - 18x + 9\) is: \[ (5x - 3)(x - 3) \]