Dr Loh’s Method

‘Normally, when we do a factoring problem, we are trying to find two numbers that multiply to 12 and add to 8,’ Dr Loh said.

Those two numbers are the solution to the quadratic, but it takes students a lot of time to solve for them, as they are often using a guessand-check approach.

Instead of starting by factoring the product, 12,

Loh starts with the sum, 8. If the two numbers we’re looking for, added together, equal 8, then they must be equidistant from their average. So the numbers can be depicted as 4–u and 4+u.

When you multiply, the middle terms cancel out and you come up with the equation 16–u2 = 12.

When solving for u, you’ll see that positive and negative 2 each work, and when you substitute those integers back into the equations 4–u and 4+u, you get two solutions, 2 and 6, which solve the original polynomial equation.

It’s quicker than the classic foiling method used in the quadratic formula – and there’s no guessing required.

– Courtney Linder

Suppose you have the following quadric equation to solve: