Quadratic Factorisation (Monic)
This is what a quadratic expression looks like:
ax^2+bx+c
where a, b, c are constants.
Quadratic means x is raised to the power of 2.
A monic polynomial is one where a=1.
What is factorisation? Factorisation is to find stuff that multiplies to get the quadratic. It goes im this form:
(x+p)(x+q)
You are basically packing the whole expression into two brackets that when expanded gives you the original expression. What are p and q?
p and q can be positive or negative.
The numbers p and q must multiply to get ac, and add to give b.
Let's start with an example.
x^2 + 5x + 6
First we must find what a,b,c are. a=1
b=5
c=6
Now, what multiplies to give ac?
Let's list the factors out:
1*6=6
Factors of 6:
1*6
2*3
Among these numbers we must find what adds to give us b.
b=5
Now which pair of factors add to give 5?
1+6=7 Nope not this pair
2+3=5 Yes! Found it!
Now simply put these two numbers into two brackets with x in them:
(x+3)(x+2)
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Here's one with negatives:
x^2+3x-4
1) Find a,b,c
a=1
b=3
c=-4
2) Find the factors of ac
ac=1*-4=-4
Factors:
1*-4
-1*4
2*-2
3) Find which pair of factors add up to get b
b=3
2-2=0 Not this pair
1-4=-3 Nope not this pair
4-1=3 GOTCHA!
Now we know the two numbers that are in the brackets must be 4 and -1.
4) Stuff the number back into the brackets
(x+_)(x+_)
Yep put them in in any order you like BUT FOLLOW THE SIGNS!
(x+4)(x-1)
That's it! Questions? Send us an email!
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