Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

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, in the expression 3x^2 + 5x^2, both terms are like terms because they both contain x^2.

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 = (3 + 5)x = 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 the polynomial 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 a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What does it mean to simplify a polynomial?

Back

Simplifying 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 from each polynomial. For example, (2x + 3) + (4x + 5) = (2x + 4x) + (3 + 5) = 6x + 8.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x + 4) - (2x + 1) = (3x - 2x) + (4 - 1) = x + 3.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

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, 3x is a monomial, while 3x + 2 is a polynomial.