Question

Formula for factorising using common method pls tell me

Answer 1

Answer

I think you are looking for Factoring out the greatest common factor (GCF)

To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor.

Example

2x^3 + 8x^2 + 4x

We can factor 2 from our coefficients because all three “terms” (between the + or -) can be divided by 2.

We can also see each term has at least 1 x so we can divide each term by x

So your GCF is 2x. We write that out front and go to step 2.

2x ( Answer will go here)

Step 2 is to divide the polynomial by the GCF of 2x. Remember when we divide the variable we subtract the exponents

(2x^3 ÷ 2x) + ( 8x^2 ÷ 2x) + (4x ÷ 2x)

= x^2 + 4x +2 plug this into your answer ( ) with your GCF out front

2x ( x^2 + 4x + 2) would be your answer.

Remember you must be able to divide each term with your GCF. If one term doesn’t have x, you can’t have x in your GCF.

I hope this is what you were looking for

Answer 2

Explanation:

there is no common method, as there are things in various forms that can be multiplied to each other.

you need to assemble experience in multiplying various forms of terms and expressions to remember, what you can aim for.

there are some basic principles like

(a² - b²) = (a + b)(a - b)

(a³ - b³) = (a - b)(a² + ab + b²)

a² + 2ab + b² = (a + b)² = (a + b)(a + b)

and, and, and

also, often you need to try to add or remove some terms to make an expression a perfect multiplication result.

like

x + xy + y = 0

x(1 + y) + y = 0

x(1 + y) + y + 1 = 0 + 1

x(1 + y) + (1 + y) = 1

(1 + y)(x + 1) = 1

or you need to split some things up to create perfect multiplications.

like

x³ + x² = 12

x³ + x² - 12 = 0

x³ + x² - 8 - 4 = 0

x³ + x² - 2³ - 2² = 0

(x³ - 2³) + (x² - 2²) = 0

remember, what we just listed above :

(x - 2)(x² + 2x + 4) + (x - 2)(x + 2) = 0

(x - 2)(x² + 2x + 4 + x + 2) = 0

(x - 2)(x² + 3x + 6) = 0

and so on.

there are many functions like trigonometric functions (sine, cosine, ...), logarithms, ...

there are not just multiplications and exponents.

sure, it is more standardized, when we are only dealing with a squared function like

4x² - 12x + 9

which is easy to see is the same as

(2x - 3)²

or more interesting

6x² - 23x + 20

which would be

(2x - 5)(3x - 4)

and we can get such things only by starting in general by saying this is

(ax + b)(cx + d)

multiply this out and find the factors of in this case 6, 23 and 20 and try the combinations.

so, long story short, there is no general method, formula or something like this. you need to get a feeling what approach could work in a given situation.