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Factorization is a method of writing numbers as the product of their factors or divisors.
<em><u>Solution:</u></em>
<em><u>Factorisation:</u></em>
Factorization is a method of writing numbers as the product of their factors or divisors.
In other words we can say, Finding what to multiply together to get an expression.
It is like "splitting" an expression into a multiplication of simpler expressions.
<em><u>Methods of factorisation:</u></em>
- Factoring out the GCF
- The sum-product pattern
- The grouping method
- The perfect square trinomial pattern
- The difference of squares pattern
<em><u>Factoring out the GCF:</u></em>
This methods means that factoring out common factors
For example:
This can be used when each term in given expression shares a common factor
<em><u>The sum-product pattern</u></em>
A quadratic equation may be expressed as a product of two binomials
For example:
This method can be used for quadratic equations of form
<em><u>The grouping method</u></em>
If the polynomial is of the form and there are factors of ac that add up to b , we can use this method
For example:
<em><u>The perfect square trinomial pattern</u></em>
If the first and last terms are perfect squares and the middle term is twice the product of their square roots , we can use this method
For example:
<em><u>The difference of squares pattern</u></em>
If the expression represents a difference of squares, we can use this method
Because
For example:
The table models an exponential relationship, and the equation of the table is
The table of values is given as:
x 0 1 2 3 4
y 4 2 1 1/2 1/4
The above table shows an exponential model
An exponential model is represented as:
When x = 0 and y = 4, we have
Evaluate
a = 4
When x = 1 and y = 2, we have
Evaluate
Substitute 4 for a
4b = 2
Divide both sides by 4
b = 1/2
Substitute 4 for a and 1/2 for b in
Hence, the equation of the table is
Read more about exponential models at:
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