1, the monomial is a formula composed of the product of a number and a letter. Like x, 2x, 3x? Are all monomials, where x is the letter part, 2x and 3x? This is the digital part. The coefficient of the monomial refers to the number part, and the index of letters refers to the number of times the letters appear in the monomial.
2. Polynomial is a formula composed of several monomials. Like 3x? +2x+ 1 is a polynomial composed of 3x? , 2x and 1. In polynomials, each monomial is connected by addition or subtraction.
3. Polynomial can be expressed as (x 1, x2, ..., xn), where a is the coefficient of polynomial, x 1, x2, ..., xn is the independent variable of polynomial. Each term of a polynomial can be regarded as a function of this independent variable.
4. In polynomial, the degree of each term must be the same, and the coefficient of the highest term cannot be 0. Like 3x? +2x？ +x+ 1 is a legal polynomial, but 3x? +2x+ 1 is not a legal polynomial because the coefficient of its highest term is 0.
The difference between monomial and polynomial
1, a monomial is a formula composed of the product of a number and a letter, and a polynomial is a formula composed of several monomials. In other words, a monomial is a basic mathematical expression, while a polynomial is a more complex expression composed of multiple monomials.
2. The letter index in a single item refers to the number of times letters appear in a single item, and the letter index of each single item in a polynomial can be different. For example, in the monomial 3x? In, the exponent of x is 2, while in the polynomial 3x? +2x+ 1, the first monomial 3x? The index of X in the second item 2x is 2, the index of X in the second item 2x is 1, and there is no letter part in the third item 2x.
3. Each monomial in the polynomial is connected by addition or subtraction. In polynomial, the coefficient and letter index of each term must be the same, but the coefficient can be negative. Like a polynomial 3x? +2x？ -x+ 1, the first monomial 3x? The coefficient of is 3, and the second monomial is 2x? The coefficient of is 2, the coefficient of the third term -x is-1, and the coefficient of the fourth term 1 is 1.
4. The operation modes of monomial and polynomial are also different. In the monomial, we only need to operate on numbers and letters, while in the polynomial, we need to operate on each monomial and then add or subtract them to get the final result.