Mixed 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 does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of the degree of the terms. For example, 4x^3 - 2x^2 + 5 is in standard form.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine 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 the polynomial 5x^4 + 3x^2 - 2, the degree is 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, while 3x^2 and 4x are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What is the result of multiplying (3x - 5)(4x^2 - 2x - 3)?

Back

The result is 12x^3 - 26x^2 + x + 15.

Front

What is the sum of (4x^3 - 5x^2 + 3x) and (-2x^3 - x^2 + 6x)?

Back

The sum is 2x^3 - 6x^2 + 9x.

Front

What is the product of 6v(2v + 3)?

Back

The product is 12v^2 + 18v.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 7x^3, 7 is the coefficient.