"Factorization using common factor method" PPT courseware

"Factorization using common factor method" PPT courseware

Communication and discovery:

Find the same factors in each of the following polynomials:

1.am+bm+cm m

2. 12m2-4m3 4m2

3. 5x2y-10xy 5xy

Common factor: The same factor that all terms in a polynomial contain.

How to find common factors:

1. When each coefficient is an integer, find ( ) of each coefficient.

2. Find the ( ) power of each item with the same letter.

Explore and think:

1. Find the product of the following integer multiplications:

①, m(a+b+c)=

②、5y2(y+4)=

2. I believe you can quickly tell the following results:

①、ma+mb+mc=m(a+b+c)

②、5y3+20y2=5y2(y+4)

Factorization: converting a polynomial into the product of several integers.

The above method of factorization is called the common factor method.

Factoring and multiplication of integers have a reciprocal relationship.

The essence of factorization:

1. The result of factorization must be in the form of a product.

2. Factorization and integer multiplication are inverse operations of each other.

Typical example 1:

Factor the following equations:

(1)3a2+12a; (2)-4x2y-16xy+8x2.

Solution: (1) 3a2+12a

=3a.a+3a.4

=3a(a+4)

Note: When the coefficient of the first term of the polynomial is negative, the negative sign should generally be brought out, and the signs of each term of the polynomial should be changed.

The key to correctly finding the common factors of the polynomials is:

Definite coefficient: The coefficient of a common factor is the greatest common divisor of the coefficients of the polynomial.

Definite letters: The letters are the same letters contained in each term of the polynomial.

Definite exponent: The exponent of the same letter takes the smallest one among the items, that is, the lowest power of the letter

Typical example 2

Factor the following equations:

(1)a(m-6)+b(m-6); (2)3(a-b)+a(b-a).

Solution: (1) a(m-6)+b(m-6)=(m-6)(a+b)

(2)3(a-b)+a(b-a)=3(a-b)-a(a-b)=(a-b)(3-a)

Summary and reflection

1. What is factorization?

2. Method of determining common factors:

1) Definite coefficient 2) Definite letter 3) Definite exponent

3. Steps to decompose factors using the common factor method:

The first step is to find the common factors;

The second step is to propose common factors (convert the polynomial into the product of two factors)

4. Issues that should be paid attention to when decomposing factors using the common factor method:

(1) All common factors must be mentioned;

(2) Be careful not to miss it;

(3) The first term of the completed polynomial should be positive.

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"Factorization using common factor method" PPT courseware 2:

"Using the Common Factor Method for Factorization" PPT Courseware 2 Cooperation and Exploration 1. Find the product of the following integer multiplications: ①, m(a+b+c)=ma+mb+mc ②, 5y2(y+4 )=5y3+20y2 2. I believe you can quickly tell the following result: ①, ma+mb+mc=m(a+b+c) ..