Simplify and Divide Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What does it mean to simplify a polynomial?

Back

To simplify a polynomial means to combine like terms and reduce the expression to its simplest form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x + 1) + (2x^2 - 4x - 5) = 5x^2 - 2x - 4.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

What is the degree of a polynomial?

Back

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

Front

What is the process of polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial, similar to long division with numbers. It involves dividing, multiplying, and subtracting until the remainder is less than the divisor.

Front

What is the result of dividing (2x^2 + 3x + 1) by (x + 1)?

Back

The result is 2x + 1 with a remainder of 0.

Front

What is a remainder in polynomial division?

Back

A remainder is what is left over after dividing a polynomial by another polynomial when the division is not exact.

Front

How do you identify errors in polynomial division?

Back

To identify errors in polynomial division, check each step of the division process, ensuring that the multiplication and subtraction are performed correctly.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.