Factorising Quadratics

Factorising quadratics is basically putting them in brackets. In this section we will look at two different ways of factorising quadratics( for simple and complex ones) and when they should be used.

Note/ sometimes a quadratic cannot be factorized using whole numbers, this is when you must use the quadratic equation to find the values of x. See my earlier post and c++ program

Simple type

Use when there is no coefficent of x²

eg)x²+2x-8

start by opening 2 brackets with an x in each

(x )(x )

put the first sign in the first bracket. If the second sign is + put the same sign in both, if its - put the opposite sign in the second bracket

(x+ )(x- )

find the 2 numbers that will add(if both signs in brackets are +) or subtract(if the signs in the brackets are different) to make the middle number(2) and multiply to make the end number(8)

(x+4)(x-2)

and thats your quadratic factorized

Complex Type

Use when there is a coefficent of x²

eg) 8x²-14x-15

Before we can open brackets we need to split up the 14x

8x² ?x ?x-15

the rule for the signs is the same as in the simple case, put the first sign before the first x term. If the second sign is + put the same sign in both, if its - put the opposite sign before the second x term

8x²-?x+?x-15

we also use the same rule for the to coefficients of x, they must add or subtract to make the middle number(14) but they must times to make the end number times the first(15×8=120)

8x²-20x+6x-15

we then take out the common factor of the first 2 terms(4x)

4x(2x-5) + 6x -15

we use the bracket(2x-5) as the common factor for the second 2 terms and find what we need to multiply by(3)

4x(2x-5)+3(2x-5)

we then take the 2 numbers in front of the brackets(4x and 3) as our second bracket

(4x+3)(2x-5)

and there we have a fully factorized quadratic