Polynomials are algebraic expressions consisting of variables and constants. A polynomial's degree is determined by the highest power of its variable. In division of polynomials, we identify terms like the dividend (the expression being divided), the divisor (the expression dividing), the quotient (the result), and the remainder. Polynomials are classified by the number of terms: monomials have one term, binomials have two, and trinomials have three. Understanding these fundamental parts is essential for mastering algebraic operations.
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A polynomial is an expression consisting of variables and coefficients with non-negative integer exponents. The expression 2x + 1 (where x is raised to the power of 1) satisfies this definition.
Question 2
DB ID: 1208
Points: 1
Which of the following is a polynomial?
Explanation
Option a is a polynomial because all exponents of the variable x are non-negative integers. Option b is not a polynomial because the variable y appears in the denominator, which implies a negative exponent (y-3).
Question 3
DB ID: 1209
Points: 1
x-3 + 2x2 - 7. The given expression is a polynomial.
Explanation
Polynomials cannot have negative exponents for their variables. The term x-3 prevents this expression from being a polynomial.
Question 4
DB ID: 1210
Points: 1
From the given illustration. What is the remainder?
Explanation
In the long division shown, the final value at the bottom after subtraction is 0, which represents the remainder.
Question 5
DB ID: 1211
Points: 1
From the given illustration. What is the divisor?
Explanation
The divisor is the expression you are dividing by. In the long division format, it is the term placed outside the division symbol, which is x + 4.
Question 6
DB ID: 1212
Points: 1
What is the process used to obtain the 2nd line?
Explanation
In polynomial long division, the line beneath the dividend is obtained by multiplying the current term of the quotient (5x) by the entire divisor (x + 4).
Question 7
DB ID: 1213
Points: 1
In the expression \(\frac{2x^2 + 5x - 23}{x+5}\), the dividend is:
Explanation
The dividend is the quantity that is being divided. In a fraction representing division, the numerator is the dividend.
Question 8
DB ID: 1214
Points: 1
Which of the following is a polynomial expression?
Explanation
A polynomial expression must have non-negative integer powers. Option a has a fractional power (1/2), and option c has a variable in the denominator. Option b contains only integer powers.
Question 9
DB ID: 1215
Points: 1
Which of the following polynomials is a binomial?
Explanation
A binomial is a polynomial consisting of exactly two terms. 5x - 1 has two terms, making it a binomial.
Question 10
DB ID: 1216
Points: 1
Which of the following polynomials is a trinomial?
Explanation
A trinomial is a polynomial consisting of exactly three terms. The expression 3x + 5y2 - 3 has three terms separated by addition or subtraction.
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