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Factorisation:
It is the reverse process of multiplication.
Example:
The factors \(x+1\) and \(x+2\) are multiplied as follows to get a quadratic polynomial.
\(x+1\) \(\cdot\) \(x+2\) \(=\) \(x^2 + x + 2x + 2\)
\(=\) \(x^2 + 3x + 2\)
\(x^2 + 3x + 2\) is factorised to get the factors \(x+1\) and \(x+2\).
Ways of factorisation:
There are two ways of factorization
- By factoring out the common term.
Example:
Factorise \(ax^2 + bx\).
Solution:
Here \(x\) is the common term in the polynomial \(ax^2 + bx\).
Factor out \(x\) from the polynomial \(ax^2 + bx\).
\(ax^2 + bx\) \(=\) \(x(ax + b)\)
The factors of \(ax^2 + bx\) are \(x\) and \(ax + b\).
- By grouping the items in an expression.
Example:
Factorise \(ax + a + bx + b\).
Solution:
Group the identical terms in the polynomial \(ax + c + bx + b\).
\(ax + a + bx + b\) \(=\) \((ax + a) + (bx + b)\)
\(=\) \(a(x + 1) + b(x + 1)\)
Factor out the common terms in the above expression.
\(ax + a + bx + b\) \(=\) \((x + 1)(a + b)\)
The factors of \(ax + a + bx + b\) are \((x + 1)\) and \((a + b)\).
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