Factoring

Given a quadratic equation : ax2 + bx + c

Can be factored into (mx+p)(nx+q)

=mnx2 + mxq + pnx + pq

=(mn)x2 + (mq+pn)x+pq

=mn=a, mq+pn=b, pq=c



General Steps to solve by factoring

- Create a factor for all factor pairs of c

- A factor pairs is just two numbers that multiply and give you ‘c’

- Out o all the factor pairs from step 1, look for the fair (if it exist) that add up to b

- Note : if the pair does not exist, you must either complete the square or use the quadratic formula.

- Insert the pair you found in step 2 into two binomials

- Solve each binomial for zero to get the solutions of the quadratic equation.



If ax2 + bx + c then (x + h)(x + k)

If ax2 + bx –c or ax2 +bx-c then (x – h)(x + k)

If ax2 – bx +c then (x - h)(x – k)



Example 1 : x2 + 5x + 6 = 0

This can be factored into (x + 2)(x + 3) = 0.

So the solution must be x = -2 and x = -3.