Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What are the different types of polynomials based on the number of terms?

Back

1. Monomial: 1 term (e.g., 5x) 2. Binomial: 2 terms (e.g., x + 2) 3. Trinomial: 3 terms (e.g., x^2 + x + 1) 4. Polynomial with more than 3 terms (e.g., x^3 + 2x^2 + x + 1) is simply called a polynomial.

Front

How do you classify a polynomial by its degree?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What is the degree of the polynomial 5x^4 - 3x^2 + 2?

Back

The degree is 4, as the highest power of x is 4.

Front

Simplify the expression: -3x^2(7x^2 - x + 4)

Back

-21x^4 + 3x^3 - 12x^2.

Front

How many terms are in the polynomial 3x^3 - 2y + 8x - 16?

Back

There are 4 terms.

Front

Classify the polynomial 12 by the number of terms.

Back

Monomial.

Front

Classify the polynomial 3x^3 - 6x by its degree.

Back

Cubic.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as x + 5.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms, such as x^2 + 3x + 2.