This is the most basic thing. As long as the common factor is put forward, everyone will know, so I won't say much.

2. Perfect square

a^2+2ab+b^2=(a+b)^2

a^2-2ab+b^2=(a-b)^2

When you see the square of two numbers in the formula, you should pay attention to find out whether the product of two numbers is twice, and if so, follow the above formula.

3. Variance formula

a^2-b^2=(a+b)(a-b)

Learn this by heart, because you can add items when matching complete squares. If you subtract a number from the previous complete square, you can decompose it again with the square difference formula.

4. Cross multiplication

x^2+(a+b)x+ab=(x+a)(x+b)

This is very practical, but it doesn't work well.

When the above method cannot be used for decomposition, cross multiplication can be used.

For example: x 2+5x+6

First of all, there are quadratic terms, linear terms and constant terms, and cross multiplication can be used.

The coefficient of the first term is 1, so it can be written as 1* 1.

The constant term is 6. It can be written as1* 6,2 * 3,-1 *-6, -2 *-3 (decimals are not recommended).

And then arrange it like this

1 - 2

1 - 3

The position of the next column can be exchanged as long as the product of these two numbers is a constant term. )

Then multiply diagonally, 1*2=2, 1*3=3. Then add products. 2+3=5, which is the same as the coefficient of the first term (it may not be equal, so we should try again at this time), so it can be written as (x+2)(x+3) (do it horizontally at this time).

I'll write a few more formulas, and the landlord will think for himself.

x^2-x-2=(x-2)(x+ 1)

2x^2+5x- 12=(2x-3)(x+4)

In fact, the most important thing is to use it for yourself. In fact, the above methods can be used together, and practice is always better than others.

By the way, if b 2-4ac of a formula is less than 0, then this formula cannot be decomposed under any circumstances (in the real number range, B is the coefficient of the first term, A is the coefficient of the second term, and C is a constant term).

These methods are generally applicable to the case that the highest order is quadratic!

Factorial theorem: trial and error method. When this formula is zero, x=a, and x-a is a factor of this formula. Using big division, just like the division of numbers, can be simplified. But it is not recommended.