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, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 5x^4 + 3x^2 - 7, the degree is 4.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

How do you subtract polynomials?

Back

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

Front

What is the sum of cubes?

Back

The sum of cubes is a special product that states a^3 + b^3 = (a + b)(a^2 - ab + b^2). For example, x^3 + 8 = (x + 2)(x^2 - 2x + 4).

Front

What is the product of a monomial and a polynomial?

Back

To find the product of a monomial and a polynomial, distribute the monomial to each term in the polynomial. For example, 3x(2x^2 + 4x) = 6x^3 + 12x^2.

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

How do you factor a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) and use it to rewrite the polynomial. For example, 6x^2 + 9x = 3x(2x + 3).