What is factoring and what is factoring

The factorization method is a method of following a quadratic equation.

Factorization is a method used in mathematics to solve higher-order unary equations. The method of factoring the number (including unknown numbers) on one side of the equation to 0 by moving it, and turning the other side of the equation into the product of several factors, and then making each factor equal to 0 to find its solution is called factorization.

Factorization, an algebraic term, refers to the process and result of representing a polynomial as the product of several polynomials. The process of expressing the polynomial on p as such a product is called the factorization of the polynomial, referred to as the factorization of the polynomial (or factorization).

Factorization is a method used in mathematics to solve higher-order unary equations. The method of factoring the number on one side of the equation to 0 by moving the terms, and the product of several factors on the other side of the equation, and then making each factor equal to 0 to find the solution.

The deformation of a polynomial into the product of several integers is called factoring the slag collapse term, also known as factoring. Factorization is the basis of identity deformation, which plays an important role as a powerful tool in mathematics and a mathematical method in solving problems in algebra, geometry, trigonometry, etc. In addition to the method of extracting common factors, formula method, group decomposition method, cross multiplication, etc., which are introduced in middle school textbooks, there are also methods such as using split terms to add terms, root decomposition, commutation, pending coefficients, and so on.

8 Factoring – What is Factoring.

What are the ways to defactor factors?

Definition: Reducing a polynomial to the product of several simplest integers, this identity transformation is called factorization.

For example: x +2xy-3y = (x+3y)(x-y).

Factorization: Formula method. Items of the same kind that can be merged should be merged.

2x(x-1)+(x-1)=0, 2x*(x-1)+1*(x-1)=0

Extract the common factor (x-1), (x-1) (2x+1) = 0

2x and 1 are two (x-1) factors connected by a plus sign in the middle.

1.Extract the common factor.

This is the most basic. It's just that if there is a common factor, it will be brought up, and everyone will know this, so I won't say much.

2.Perfectly squared.

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

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

If you see that there are two numbers squared in the formula, you should pay attention to it, find out if there is twice the product of the two numbers, and if so, follow the above formula.

3.Square Difference Formula.

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

This should be memorized, because it is possible to add terms when matching perfect squares, and if the front is perfectly squared, and then subtract a number, you can use the square difference formula to break it down.

4.Cross multiplication.

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

This one is very practical, but it is not easy to use.

When the above method cannot be used to decompose, the lower cross multiplication method can be used.

Example: x 2 + 5 x + 6

First of all, it is observed that there are quadratic terms, primary terms, and constant terms, which can be multiplied by crosses.

The coefficient of the primary term is 1So it can be written as 1*1

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

Then arrange it like this.

The positions of the following columns can be reversed, as long as the product of these two numbers is a constant term).

Then multiply diagonally, 1*2=2, 1*3=3Add the product again. 2+3=5, which is the same as the coefficient of the primary term (it may not be equal, in this case another attempt should be made), so it can be written as (x+2) (x+3).

At this point, just come sideways).

I'll write a few more formulas, and the landlord will figure it out 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 yourself, the above methods can actually be used together, and practice is always better than teaching others.

By the way. If the b 2-4ac of an equation is less than 0, the formula cannot be decomposed in any way (in the range of real numbers, b is the coefficient of the first term, a is the coefficient of the quadratic term, and c is the constant term).

These methods are generally applicable when the highest order is secondary!

9(2x+3)²=4（2x-5）²

9 (4x +12x + 9) = 4 (4x -20x + 25) 36x +108x + 81 = 16x -80x + 100 can be obtained.

20x²+188x-19=0

Factorization is available.

2x+19）（10x-1）=0

2x+19=0 or 10x-1=0

The solution yields x1=-19 2 or x2=1 10