"Integral" PPT courseware

Description

"Integral" PPT courseware

think carefully

(1) Is "9" a monomial? Is "a" a monomial?

(2) Is 3/x a monomial? Is x/3 a monomial?

Are "2x+1" and "a–b" monomials?

(3) Is 4a²b²c² a monomial?

(4) Is S=πr² a monomial?

The algebraic expression formed by multiplying numbers and letters (or letters and letters) is called a monomial.

Notice:

1. A single number or letter is also a monomial.

2. There is only a product operation relationship between monomial numbers and letters.

3. Monomial numeric factors and letters may be one or more.

Fill it out

The coefficient of �1�–2a²b is____;

The coefficient of �2�2πr is____;

The coefficient of �3�–m is____;

coefficient of monomial

We call the numerical factors in a monomial the coefficients of the monomial.

Note: (1) Pi is a constant and cannot be discarded when finding the coefficient.

(2) When the coefficient of a monomial is 1 or –1, “1” is usually omitted, but do not mistake it for 0, such as a², –abc;

(3) When the coefficient of the monomial is a mixed number, it should be written as an improper fraction. For example, 1 1/4x²y should be written as 5/4 x²y.

(4) The coefficient of the monomial includes the previous sign.

Polynomial: The sum of several monomials.

Terms of a polynomial: Each monomial in a polynomial.

Constant term: In a polynomial, a term that does not contain letters.

The terms of polynomials: A polynomial containing several terms is called a term.

Degree of polynomial: In a polynomial, the degree of the highest term is the degree of the polynomial.

For example: 3x2-2x+5 contains three items, they are:

The degree of 3x2 is 2

-2x times is 1

5 times is 0

The highest degree term among the three terms is the first term, which is degree 2, so this is a quadratic trinomial.

Example: Indicate the terms and degrees of the following polynomials

(1) a3–a2b+ab2 –b2; (2) 3n4 –2n2+1

Solution: (1) The terms of the polynomial a3–a2b+ab2 –b2 are: a3, –a2b, ab2, –b2. The degree of each term in the polynomial is 3, so the degree of the polynomial is 3.

(2) The terms of the polynomial 3n4 –2n2+1 are: 3n4, –2n2, 1. The degree of the first term in the polynomial is 4, the degree of the second term is 2, and the degree of the third term is 0, so the degree of this polynomial The number of times is 4.

feedback exercise

True or false:

x2–2xy+y2 is a sixth degree trinomial ( )

The degree of a3 –5a2b2+4a2b –6b3 is 3 ( )

The terms of the polynomial 2x2 –3xy+y2 include 2x2, 3xy, y2 ( )

Notice:

1. Each term of a polynomial includes the symbol preceding it.

2. Method to find the degree of polynomial:

I first calculate the degree of each monomial,

II Then choose which monomial has a higher degree. The degree of the term with the highest degree is the degree of the polynomial.

Extension exercises

1. The coefficient of monomial m2n2 is _______, degree ______, m2n2 is a monomial of degree ____.

2. The polynomial x+y-z is the sum of the monomials ____, ____, ____, and it is a ____ degree ____ term.

3. The constant term of the polynomial 3m3-2m-5+m2 is _____, the linear term is _____, and the coefficient of the quadratic term is _____.

4. If -5xym-2 is a 4th degree monomial, then m=____.

Class summary

Integer

Monomials (products of numbers and letters)

Coefficients: Numeric factors in a monomial (including preceding symbols)

Degree: the sum of the exponents of all the letters in the monomial

Polynomial (sum of several monomials)

Terms: each monomial in the polynomial

Degree: the degree of the highest degree term in a polynomial

nth degree nnomial

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Update Time: 2024-11-19

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