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, along with coefficients. For example, 2x^2 + 3x - 5 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 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 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 or the FOIL method. 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 equal to a^2 + 2ab + b^2. For example, (2x + 3)^2 = 4x^2 + 12x + 9.

Front

How do you factor a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) and use methods like grouping or applying special formulas (e.g., difference of squares).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where a^2 - b^2 = (a - b)(a + b). For example, x^2 - 9 = (x - 3)(x + 3).

Front

What is the sum of cubes formula?

Back

The sum of cubes formula is 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 sum and a difference?

Back

The product of a sum and a difference is given by a^2 - b^2 = (a + b)(a - b). For example, (x + 5)(x - 5) = x^2 - 25.