Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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.

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of irreducible factors, meaning it cannot be factored further over the set of real numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

Front

What is the sum of cubes formula?

Back

The sum of cubes can be factored using the formula a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the product of sums and differences?

Back

The product of sums and differences states that (a + b)(a - b) = a² - b².

Front

How do you factor a quadratic polynomial in the form ax² + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Use these numbers to split the middle term and factor by grouping.

Front

What is the role of the leading coefficient in factoring?

Back

The leading coefficient (the coefficient of the highest degree term) affects the methods used for factoring, especially in quadratics, as it can influence the factors' values.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.