Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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 and 5x are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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 + 5, the degree is 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 2x^3 + 3x^2 + x + 5.

Front

What is the process of multiplying polynomials?

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 (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6.

Front

How do you simplify the expression (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

The simplified expression is 5b^4 - 2b^3 + 4.

Front

What is the result of combining like terms in (5x + 2) + (4x + 5)?

Back

The result is 9x + 7.

Front

What is the result of multiplying (4x + 3)(2x - 1)?

Back

The result is 8x^2 + 2x - 3.