Operations on 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, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from each polynomial. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4x) - (2x^2 + 5x) = (3x^2 - 2x^2) + (4x - 5x) = x^2 - x.

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, (a + b)(c + d) = ac + ad + bc + bd.

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, and 3x + 2 is a polynomial.

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

How do you simplify the expression 2x^3 + 3x^3?

Back

To simplify, combine like terms: 2x^3 + 3x^3 = 5x^3.

Front

What is the result of multiplying (5n - 8)(5n + 8)?

Back

The result is 25n^2 - 64, using the difference of squares formula.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).

Front

What does it mean to evaluate a polynomial?

Back

Evaluating a polynomial means substituting a specific value for the variable and calculating the result. For example, for p(x) = 2x^2 + 3, if x = 2, then p(2) = 2(2^2) + 3 = 11.