Polynomials: Mixed Practice (1-16)

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 4x^3 is a monomial.

Front

How do you divide a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. For example, (2x^8 - 8x^2 - 28x) ÷ 2x = x^7 - 4x - 14.

Front

What is the result of (4x^2 + x) - (x^2 + 2x)?

Back

The result is 3x^2 - x.

Front

How do you find the sum of two polynomials?

Back

To find the sum, combine like terms. For example, (2x^2 + 5x - 7) + (3 - 4x^2 + 6x) = -2x^2 + 11x - 4.

Front

What is the process of polynomial multiplication?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What is the result of (5x + 1)(x + 4)?

Back

The result is 5x^2 + 21x + 4.

Front

What are like terms in a polynomial?

Back

Like terms are terms 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 polynomial. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial. For example, in 3x^4 + 2x^3 - x, the leading coefficient is 3.