Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a sum or difference.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is a like term?

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 expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the process of simplifying a polynomial?

Back

Simplifying a polynomial involves combining like terms and reducing the expression to its simplest form.

Front

What is the result of (5x + 2)(x^2 - 3x + 6)?

Back

The result is 5x^3 - 13x^2 + 24x + 12.

Front

How do you subtract polynomials?

Back

To subtract polynomials, change the signs of the terms in the polynomial being subtracted and then combine like terms.

Front

What is the result of (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

The result is 5b^4 - 2b^3 + 4.