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 Greatest Common Factor (GCF)?

Back

The GCF of two or more numbers is the largest number that divides all of them without leaving a remainder.

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, identify and factor out the GCF first, then apply techniques such as grouping, using special products, or trial and error for remaining factors.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states: a^2 - b^2 = (a - b)(a + b).

Front

Factor the polynomial: 81m² - 1

Back

(9m - 1)(9m + 1) - This is a difference of squares.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as a² + 2ab + b² = (a + b)².

Front

Factor the polynomial: 3x² + 18x + 15

Back

3(x + 5)(x + 1) - First factor out the GCF, then factor the quadratic.

Front

What is the sum of cubes?

Back

The sum of cubes is a special factoring pattern that states: a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the difference of cubes?

Back

The difference of cubes is a special factoring pattern that states: a³ - b³ = (a - b)(a² + ab + b²).