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 consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or terms.

Front

How do you factor a polynomial with a GCF?

Back

To factor a polynomial with a GCF, first identify the GCF of all the terms, then divide each term by the GCF and express the polynomial as the product of the GCF and the resulting polynomial.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.

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

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are the two numbers.

Front

What is the sum of cubes formula?

Back

The sum of cubes formula is a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the product of a sum and difference?

Back

The product of a sum and difference is a² - b² = (a + b)(a - b).

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, first factor out the GCF, then look for patterns such as difference of squares, perfect square trinomials, or apply the quadratic formula if necessary.