"Factorization" PPT

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"Factorization" PPT

Part One: Fill it out

Can you find the connections and differences between these two sets of equations? What are the characteristics of their left and right sides?

Features: Convert the form of the product of integers into the form of the sum of polynomials.

Features: Convert the sum of polynomials into the product of several integers.

definition

Generally speaking, converting a polynomial into the product of several integers is called factorization. Sometimes we also call this process factorization.

Factoring PPT, Part 2: Understanding Concepts

Determine which of the following expressions are integer multiplications? Which ones are factoring?

(1).x2-4y2=(x+2y)(x-2y)

(2).2x(x-3y)=2x2-6xy

(3).(5a-1)2=25a2-10a+1

(4).x2+4x+4=(x+2)2

(5).2πR+ 2πr= 2π(R+r)

Factoring PPT, Part 3: Think about it

Through what you just learned, can you tell what the relationship is between factorization and integer multiplication?

Characteristics of multiplication of integers: converting the form of the product of integers into the form of the sum of polynomials.

Characteristics of factorization: Convert the sum of polynomials into the product of several integers.

Conclusion: Factorization of polynomials and multiplication of integers are two identical deformations in opposite directions, and they are reciprocal processes.

Factoring PPT, Part 4: Practice:

1. Check whether the following factorization is correct.

(1)m2+mn=m(m+n)

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

(3)x2-x-2=(x+2)(x-1)

2. Calculate each of the following problems and explain your algorithm.

(1)87 2 + 87 ×13

(2) 1012-99 2

Factoring PPT, Part 5: Summary

Factoring and multiplication of integers are reciprocal processes.

Pay attention to the following points when factoring:

1. The object of decomposition must be a polynomial.

2. The result of decomposition must be in the form of the product of several integers.

3. Decompose until it can no longer be decomposed.

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for seventh grade volume 2, factoring PPT download, .PPT format;

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Update Time: 2024-06-28

This template belongs to Mathematics courseware Hebei Education Edition Seventh Grade Mathematics Volume 2 industry PPT template

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