Factorisation questions and answers pdf
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How to factorise quadratics!
Factoring in Algebra
Factors
Numbers have factors:
And expressions (like x2+4x+3) also have factors:
Factoring
Factoring (called "Factorising" in the UK) is the process of finding the factors:
Factoring: Finding what to multiply together to get an expression.
It is like "splitting" an expression into a multiplication of simpler expressions.
Example: factor 2y+6
Both 2y and 6 have a common factor of 2:
So we can factor the whole expression into:
2y+6 = 2(y+3)
So 2y+6 has been "factored into" 2 and y+3
Factoring is also the opposite of Expanding:
Common Factor
In the previous example we saw that 2y and 6 had a common factor of 2
But to do the job properly we need the highest common factor, including any variables
Example: factor 3y2+12y
Firstly, 3 and 12 have a common factor of 3.
So we could have:
3y2+12y = 3(y2+4y)
But we can do better!
3y2 and 12y also share the variable y.
Together that makes 3y:
- 3y2 is 3y × y
- 12y is 3y × 4
So we can factor the whole expression into:
3y2+12y = 3y(y+4)
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