"Integral Form" PPT Courseware 2

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"Integral Form" PPT Courseware 2

How many possible combinations are there of multiplying the numbers and letters above?

An algebraic expression consisting of a number multiplied by a letter or a letter multiplied by a letter is called a monomial

Monomial An algebraic expression consisting of a number multiplied by a letter or a letter multiplied by a letter.

A single number or letter is also called a monomial.

(1) The denominators do not contain letters;

(2) Does not include numbers and letters, or addition, subtraction and square root operations of letters and letters.

Notice

(1) Pi  is a constant.

(2) If the monomial is a single letter, then its coefficient is 1. For example: the coefficient of monomial c is 1.

(3) 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;

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

degree of monomial

In a monomial, the sum of the exponents of all letters is called the degree of the monomial.

illustrate:

(1) It is all letters, not some letters;

(2) is the sum of exponents, not the product of exponents.

For example: all the letters of abc are a, b, c, their exponents are all 1, and the sum of the exponents is 1+1+1=3, so the degree of abc is 3, which is a cubic monomial.

All the letters of 4x²yz are x, y, z, and the sum of their exponents is 2+1+1=4, so the degree of 4x²yz is 4, which is a quartic monomial.

Example 2. Judgment:

(1) The coefficient of -5ab3 is 5;

(2)-a2b and a have no coefficients;

(3)-The degree of xy3z2 is 1+3+2=6;

(4) The coefficient of -b2 is -1;

(5) The degree of abc is 3;

(6)-The degree of 32x3y is 5.

concept

3x2－2x+5

An algebraic expression formed by the addition of several monomials is called a polynomial.

In a polynomial, each monomial is called a term of the polynomial. Among them, terms without letters are called constant terms.

In a polynomial, the degree of the term with the highest degree is the degree of the polynomial.

Monomials and polynomials are collectively called integers.

Example 3. Indicate the terms and degrees of the following polynomials:

(1)a3-a2b+ab2-b3; (2)3n4-2n2+1.

Solution: (1) The terms of the polynomial a3-a2b+ab2-b3 include a3, -a2b, ab2, -b3; the degree is 3.

(2) The terms of the polynomial 3n4-2n2+1 are 3n4, -2n2, 1; the degree is 4.

Notice

(1) The degree of a polynomial is not the sum of the degrees of all terms;

(2) Each term of the polynomial includes the symbol preceding it.

practice

1.3x2-4x+5 is a _____ degree _____ term.

2.(k-2)x2-5x+9 is a linear polynomial about x, then k=______.

3.4xn+6xn+1+ xn+2- xn+3 (n is a natural number)

It is a term of degree _____, in which the coefficient of the highest degree term is ____.

4. If the constant terms of polynomials x2-7x-2 and 3x2+5x+n are the same, then n-2/n=_______.

5. When m=_____, the polynomial 8x2+3mxy-5y2+ xy-8 does not contain the xy term.

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Update Time: 2024-11-20

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