Ask AI: m²+m-90 factor it

To factor the quadratic expression \(m^2 + m - 90\), you need to find two numbers that multiply to \(-90\) and add up to \(1\). Here are the steps to factor it: 1. **Identify the coefficients**: The quadratic expression is in the standard form \(ax^2 + bx + c\). For \(m^2 + m - 90\), \(a = 1\), \(b = 1\), and \(c = -90\). 2. **Look for two numbers that multiply to \(ac\) and add up to \(b\)**: In this case, \(ac = 1 \times (-90) = -90\) and \(b = 1\). 3. **Find the two numbers**: The pairs of factors of \(-90\) that add up to \(1\) are: \[ (-9) \times 10 = -90 \quad \text{and} \quad -9 + 10 = 1 \] 4. **Rewrite the middle term using these two numbers**: Split the term \(m\) into \(-9m + 10m\): \[ m^2 + m - 90 = m^2 - 9m + 10m - 90 \] 5. **Group the terms**: Group the terms into pairs: \[ (m^2 - 9m) + (10m - 90) \] 6. **Factor out the greatest common factor (GCF) from each pair**: \[ m(m - 9) + 10(m - 9) \] 7. **Factor out the common binomial factor**: Both terms have a common factor of \((m - 9)\): \[ (m - 9)(m + 10) \] So, the factored form of \(m^2 + m - 90\) is: \[ (m - 9)(m + 10) \]