Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 1 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 polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

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. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What is the process of subtracting polynomials?

Back

Subtracting polynomials involves distributing the negative sign and then combining like terms. For example, (3x^2 + 2) - (x^2 + 4) = 2x^2 - 2.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is calculated as a^2 + 2ab + b^2. For example, (2x + 3)^2 = 4x^2 + 12x + 9.

Front

What is the product of a monomial and a polynomial?

Back

To find the product of a monomial and a polynomial, multiply the monomial by each term in the polynomial. For example, -3x^2(7x^2 - x + 4) = -21x^4 + 3x^3 - 12x^2.

Front

What is the result of multiplying (3x - 6)(7x + 7)?

Back

The result is 21x^2 - 21x - 42.

Front

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

Back

The simplified expression is x^2 + x + 1.

Front

What is the difference of two polynomials?

Back

The difference of two polynomials is found by subtracting the second polynomial from the first, combining like terms. For example, (5x^4 - 4x^3 - 2x^2 + x - 19) - (x^4 + 5x^3 + 8x^2 + x + 5) = 4x^4 - 9x^3 - 10x^2 - 24.