Ask AI: factor k²-13k+40

To factor the quadratic expression \(k^2 - 13k + 40\), you want to find two numbers that multiply to 40 and add up to -13. Here's how you can do that step-by-step: 1. **Write down the quadratic expression:** \(k^2 - 13k + 40\) 2. **Identify a, b, and c:** In this quadratic expression, \(a = 1\), \(b = -13\), and \(c = 40\). 3. **Find two numbers that multiply to ac and add to b:** We are looking for two numbers that multiply to \(40 \times 1 = 40\) and add up to \(-13\). After examining pairs of factors, we find that the pair \(-8\) and \(-5\) fits: \[ (-8) \cdot (-5) = 40 \] \[ (-8) + (-5) = -13 \] 4. **Rewrite the middle term using these numbers:** Rewrite \(-13k\) as \(-8k - 5k\): \[ k^2 - 8k - 5k + 40 \] 5. **Factor by grouping:** Group the terms to factor by grouping: \[ (k^2 - 8k) + (-5k + 40) \] Factor out the greatest common factor (GCF) from each group: \[ k(k - 8) - 5(k - 8) \] 6. **Factor out the common binomial factor:** \[ (k - 8)(k - 5) \] So, the factored form of \(k^2 - 13k + 40\) is: \[ (k - 8)(k - 5) \]