How do you factorise quadratics?

Answer 1

You can factor quadratics using a number of different methods, but a relatively simple way is the diamond method.

The format for a quadratic: ax2+ bx + c

Take a sample function. x2 + 2x − 15

Draw a relatively large "X" on your paper.

The top region of the diamond is the Product of (a)(c).

a = 1. c = (-15).

1(-15) = (-15).

The lower region of the diamond is the Sum of the x's, or the value of (b).

b = 2. 2 goes in the lower part of the diamond.

The regions on the sides is the space where you will write two numbers that

MULTIPLY to (a)(c) (or in this case, (-15)

ADD to (b) (in this case, 2).

In the sample function, the two numbers that multiply to (-15) and add to 2 are 5 and (-3). 5(-3) = -15. 5+(-3) = 2.

You now know that the factored form of the function x2 + 2x − 15 is written (x-3)(x+5).

You can check to make sure this is correct by distributing using the FOIL method. First, Outside, Inside, Last. Combine 'like terms' and the function should look the same as when you started out.