Respuesta :
Factorization is a method of writing numbers as the product of their factors or divisors.
Solution:
Factorisation:
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.
Methods of factorisation:
- Factoring out the GCF
- The sum-product pattern
- The grouping method
- The perfect square trinomial pattern
- The difference of squares pattern
Factoring out the GCF:
This methods means that factoring out common factors
For example:
[tex]12x^2 + 3x = 3x(4x + 1)[/tex]
This can be used when each term in given expression shares a common factor
The sum-product pattern
A quadratic equation may be expressed as a product of two binomials
For example:
[tex]x^2 + 7x + 12 = (x + 3)(x + 4)[/tex]
This method can be used for quadratic equations of form [tex]ax^2 + bx + c = 0[/tex]
The grouping method
If the polynomial is of the form [tex]ax^2 + bx + c[/tex] and there are factors of ac that add up to b , we can use this method
For example:
[tex]2x^2 + 7x + 3\\\\2x^2 + 6x + 1x + 3\\\\2x(x + 3) + 1(x + 3)\\\\(x + 3)(2x + 1)[/tex]
The perfect square trinomial pattern
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:
[tex]x^2 + 10x + 25\\\\(x + 5)^2[/tex]
The difference of squares pattern
If the expression represents a difference of squares, we can use this method
Because [tex]a^2 - b^2 = (a + b)(a - b)[/tex]
For example:
[tex]x^2 - 25\\\\x^2 - 5^2\\\\(x + 5)(x - 5)[/tex]
