Factorising? -?

Question

Can anyone explain to me in simple terms how to factorise??

Answer 1

Expanding Brackets
Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g. 2x(x + 3) = 2x² + 6x [remember x × x is x²])
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Example:
Expand (2x + 3)(x - 1):
(2x + 3)(x - 1)
= 2x² - 2x + 3x - 3
= 2x² + x – 3


Factorising
Factorising is the reverse of expanding brackets, so it is putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations.
The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

Factorising Quadratics
There is no simple method of factorising a quadratic expression. One way, however, is as follows:

Example:
Factorise 12y² - 20y + 3
12y² - 18y - 2y + 3 [here the 20y has been split up into two numbers whose multiple is 36. 36 was chosen because this is the product of 12 and 3, the other two numbers].
The first two terms, 12y² and -18y both divide by 6y, so 'take out' this factor of 6y.
6y(2y - 3) - 2y + 3 [we can do this because 6y(2y - 3) is the same as 12y² - 18y]
Now, make the last two expressions look like the expression in the bracket:
6y(2y - 3) -1(2y - 3)
The answer is (2y - 3)(6y - 1)

Example:
Factorise x² + 2x - 8
We need to split the 2x into two numbers which multiply to give -8. This has to be 4 and -2.
x² + 4x - 2x - 8
x(x + 4) - 2x - 8
x(x + 4)- 2(x + 4)
(x + 4)(x - 2)

Once you work out what is going on, this method makes factorising any expression easy. It is worth studying these examples further if you do not understand what is happening. Unfortunately, the only other method of factorising is by trial and error.

The Difference of Two Squares
If you are asked to factorise an expression which is one square number minus another, you can factorise it immediately. This is because a² - b² = (a + b)(a - b) .

Example:
Factorise 25 - x²
= (5 + x)(5 - x) [imagine that a = 5 and b = x]


Well take took a some time writing,

I really hope that It helps, Good Luck

Answer 2

Expanding Brackets
Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g. 2x(x + 3) = 2x² + 6x [remember x × x is x²]).
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Example
Expand (2x + 3)(x - 1):
(2x + 3)(x - 1)
= 2x² - 2x + 3x - 3
= 2x² + x - 3

Factorising
Factorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations.
The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

Factorising Quadratics
There is no simple method of factorising a quadratic expression, but with a little practise it becomes easier. One systematic method, however, is as follows:

Example
Factorise 12y² - 20y + 3
= 12y² - 18y - 2y + 3 [here the 20y has been split up into two numbers whose multiple is 36. 36 was chosen because this is the product of 12 and 3, the other two numbers].
The first two terms, 12y² and -18y both divide by 6y, so 'take out' this factor of 6y.
6y(2y - 3) - 2y + 3 [we can do this because 6y(2y - 3) is the same as 12y² - 18y]
Now, make the last two expressions look like the expression in the bracket:
6y(2y - 3) -1(2y - 3)
The answer is (2y - 3)(6y - 1)

Answer 3

Sure it is the process of breaking down an algebraic expression by pulling out common factors and then simplifying the remaining expression. For a second order equation or quadratic there is a neat method to help you do this-called FOIL- for first, outer, inner and last factors. In simple terms for a general quadratic you have 3 terms in the expression or equation and using FOIL you factor or sinplyfy it in the product of two term factors..watch

factor 6x^2 +10x-4
first factor out a two
2(3x^2 + 5x- 2) results, using FOIL (which becomes an automatic process that you just naturaly do after working several problems)
you get 2(3x - 1)(x + 2) multiplying the first term within each factor gives 3x^2, the outer product gives 6x, inner product gives -x and the last product gives -2 so you have
3x^2 + 6x - x - 2 = 3x^2 + 5x -2 all of which gets multiplied by and we have the original expression back...very handy way to check your work.

if we set the expression = to zero we can easily solve for two values of x that satisfy the equation we start at the final factored equation
2(3x - 1)(x + 2) = 0 divide both sieds by
and get
(3x - 1)(x + 2) = 0
take each factor one at a time set it = to o and solve for x

(3x - 1) = 0
3x = 1
x = 1/3

and (x + 2) = 0
so x = -2
and the solution set is x= -2 and x = 1/3

pretty easy huh?

Answer 4

to verify if an equation could be factorised, calculate b^2-4ac the place b is the co-effective of the skill-a million term(4 thus), a is the co-effective of skill-2 term(6 thus), and c(10 thus) is the lone quantity. sixteen-240=-224 If the respond comes out to be unfavorable, then the equation won't be able to be factorised.

Answer 5

Factoring? Is that what you mean? As in mathematics?
well the best way to apprroach it is to look to see if the number is odd or even. If it is even divide by 2 it will cut the number in half. ex 36 can be worked out easily to 18 because 18x 2 is 36 or 36 /6 is 18. the best make iT into a ratio (36/2) ,y id is [e-mail]

Answer 6

Hopefully this might help :)

Answer 7

Read the first answer.

I know it, but am no teacher, hence can't explain it.

If I tried, I'd only confuse you.

Good luck xx

AND DO NOT READ THE SECOND ANSWER!!! WTF!!!