"Factorization" Multiplication, division and factorization of integers PPT courseware

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"Factorization" Multiplication, division and factorization of integers PPT courseware

Review and Review: Multiplication of Integers

Calculate the following equations:

x(x+1)=x2 + x;

(x+1)(x－1)=x2－1.

Observation, exploration and induction

Please write the following polynomials as products of integers.

Converting a polynomial into the product of several integers is called factoring (or factoring) the polynomial.

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) (a-3)(a+3)=a2-9

(6) m2－4=(m+2)(m－2);

(7) 2πR+ 2πr= 2π(R+r).

How to factor: ma+mb+mc

Common factor: The factor that each term in a polynomial has is called the common factor of the polynomial;

Decompose the polynomial ma+mb+mc into the form m(a+b+c), where m is the common factor of each term, and the other factor (a+b+c) is ma+mb+mc divided by m This method of decomposing factors is called the common factor method.

1. Can the following polynomials be factored using the difference of squares formula? Why?

(1) x2+y2; (2) x2－y2;

(3) -x2+y2; (4) -x2-y2.

2. Factoring:

(1)a2-1/25b2; (2)9a2-4b2;

(3) x2y-4y; (4) -a4 +16.

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For more information about the PPT courseware "Factorization of Integers: Multiplication, Division and Factorization", please click the "Factorization ppt Multiplication, Division and Factorization of Integers" ppt tag.

"Factorization" PPT courseware:

Contents of the first part of the PPT courseware "Factorization": Review of old knowledge 1. How many forms are there in multiplication of integers? (1) Multiplying a monomial by a monomial (2) Multiplying a monomial by a polynomial: m(a+b+c)=ma+mb+mc ( 3) Multiply a polynomial by a polynomial: (a+b)(m+n)=am+an+bm+bn 2. Multiplication common...

"Factorization" PPT:

"Factorization" PPT Part 1 Content: Fill in Can you find the connection and difference 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 form of the sum of polynomials into...

"Factorization Method for Solving Quadratic Equations of One Variable" PPT courseware:

"Factorization Method for Solving Quadratic Equations" PPT courseware uses the factorization method to solve quadratic equations. General steps: (1) Change the right side of the equation to zero; (2) Decompose the left side of the equation into two linear equations. ________ of factors; (3) Let each factor be zero, we get..

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Update Time: 2024-11-15

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

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