Operations with Polynomials (Add, Subtract & Multiply)

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication. Example: 2x^2 + 3x - 5.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Example: (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the difference of like terms from two polynomial expressions. Example: (5x^2 + 3x) - (2x^2 + 4) = 3x^2 + 3x - 4.

Front

How do you multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in the other. Example: (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a like term?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. 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. Example: In 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. Example: In 3x^4 + 2x^3 - x, the leading coefficient is 3.

Front

What is the sum of (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The sum is -2x^2 + 11x - 4.

Front

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

Back

The sum is 4x^3 + 1x^2 - 3x + 1.

Front

What is the product of (r + 1)(r - 3)?

Back

The product is r^2 - 2r - 3.