Ask a question about mononomials and polynomials

2x^2;ax^2;-ba is a monomial, others are polynomial, mononomial:

1.The product of any letter and number (in division: dividing by a number equals multiplying the reciprocal of that number).

2.A letter or number is also called a monomial.

3.There are no unknowns in the denominator. Polynomial:

The sum of several monomials is called a polynomial (in subtraction, subtracting a number is equal to adding its opposite). Each monomial in a polynomial is called a polynomial term, and the highest number of these monomials is the degree of the polynomial.

Items that do not contain letters are called constant terms. For example, if the number of the highest term in a formula is 5, and this formula consists of 3 monomials, it is called :

Five triathletes.

In a more general definition, the sum of 1 or 0 monomials is also a polynomial. According to this definition, a polynomial is an integer. Actually, there is no theorem that only works for narrow polynomials and not for monomials :)

When 0 is used as a polynomial, the order is negative infinity.

2x^2 ax^2

2xa 3ba is a monomial.

Only multiplication is a monomial, addition is a polynomial, and the denominator contains a letter is a fraction, not an integer.

The formula composed of the product of several letters and numbers is called a monomial, such as a, 3, 3a, and 3abc are all monomials, and monomials are all integers. (There can be no letters on the denominator).

So -2x 2 , 2x 2 , ax 2 2xa 3 , -ba are all monomials.

3+2x, (x+y) 2, -1 2x), and -1+a are not monomials.

2x^2 ax^2

1/2x)ba 2xa/3

They are mononomials and judge the difference between a monomial and a polynomial: in this integer, if there is a plus or minus sign, it is called a polynomial. Of course, if there is a fraction, the denominator cannot be a letter.

SeveralMonomialThe algebraic formula that adds up the good states is calledPolynomial:(If there is subtraction: subtracting a number is equal to adding its opposite).

In mathematics, a polynomial is defined by a variable.

coefficients and addition, subtraction, multiplication, and exponentiation operations between them (non-negative integers.

power).

Each monomial in a polynomial is called a polynomial term, and the highest number of terms in these monomials is the degree of the polynomial. The term that does not contain a letter in the repatriation polynomial is called a constant term.

Use tossing and dividing.

, which tables (x) and g(x) as a combination of (x) and g(x) as a combination of (x) and g(x).

1. If the greatest common factor of (x) and g(x) is a zero-order polynomial, then (x) and g(x) are said to be mutual. Both the greatest common factor and the reciprocal generalization can be generalized to the case of several polynomials.

2. If a polynomial (x) in f[x] whose order is not less than 1 cannot be expressed as the product of two polynomials of lower order in f[x], then (x) is said to be an irreducible polynomial on f.

Monomial:

1.An algebraic formula in the form of the product of any letter and number (in division, dividing by a number equals multiplying the reciprocal of that number).

2.A letter or number is also called a monomial.

3.The denominator does not contain letters (the monomial is an integer, not a fraction) a, 5, 1x, 2xy, x 2, all refer to the monomial, and not the monomial.

The addition of multiple Zhengqing monomials is a polynomial. 2 and 3 are both mononomials, so it's a polynomial.

This equation is a monomial for the following reasons:

On the surface, this problem is composed of the addition of two monomials, which should be a multinomial formula, but 2+3 can give the result, which is simply 5, and the polynomial does not have this situation, for example, this polynomial, it can no longer be calculated, so 2+3 should be a monomial. Thank you.

Solution: (1) Analysis: does not include AB term, so -7AB+KAB=0, k=7, polynomial x 2-7AB+B 2-4a k+kab=x 2+b 2-4a 7, the highest number is 7, a total of three items;

So the polynomial is 7th trinomial, k = 7 (2) Analysis: The polynomial is a cubic binomial with respect to x, and the highest order is 3; The highest order of -(2m+n)x is 2, so 6x n is the highest term, n=3, and the binomial knows that 2m+n=0 gives m=-3 2, so 2m-n 3=-30;

3) Analysis: Without the terms of x 3 and x 2, m-3 = 0, 2n-1 = 0 to get m = 3, n = 1 2, so the original polynomial = 3x 4-3x + 1 2, when x = -1, the original formula = 1 2

In a monomial there are only multiplication and division signs, and there are no plus and minus signs.

Look at how many additions and minuses there are in a polynomial, and the number of terms before and after the addition and minus signs is the number of terms in this polynomial.

In a polynomial, the number of each monomial money is its coefficient (including the sign before the number) The so-called coefficient refers to the number before the monomial (including the conformity), and if there is no number in front of each monomial, it means that its coefficient is 1 or -1.

If there are no letters in a formula, it means that it is all numbers, it can be added and subtracted, and finally it is a constant, and the number of this formula is 0.

The term of the monomial: This is the monomial

The number of terms in a monomial: is 1 term.

How are the coefficients of polynomials determined? : For example, the coefficient of 2x-5y is 2, and -5 is considered as the addition of two monomials. The coefficients of the monomial, you should know how to find them.

If there are no numbers in the polynomial, how are the coefficients of the polynomial determined? For example, -x+y, first of all, it is the addition of two mononomials, and then -x=-1x, and the coefficient is the same thing.

If there are no letters in a polynomial, how can the number be determined? : If there are no letters in a polynomial, it is a constant term, and the order is 0.

Is the sum of a mononomial and a polynomial necessarily a polynomial?

False, e.g., the sum of the monomial -a and the polynomial a+2b is 2b, which is a monomial.

Is the sum of a polynomial to a polynomial necessarily a polynomial?

False: (x-y) + (y-2x).

x-y+y-2x

x, is a monomial.