Polynomial Operations

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 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 is the leading coefficient of a polynomial?

Back

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in the polynomial 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4) - (2x^2 + 5) = (3x^2 - 2x^2) + (4 - 5) = x^2 - 1.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property (FOIL method). For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the difference of squares?

Back

The difference of squares is a special product that states a^2 - b^2 = (a - b)(a + b). For example, 25 - 16 = (5 - 4)(5 + 4) = 1 * 9 = 9.

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, while 3x^2 and 4x are not.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

How do you factor a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) of the terms and use it to rewrite the polynomial. For example, 6x^2 + 9x can be factored as 3x(2x + 3).