Factoring Polynomials - Mini Flashcard

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 difference of cubes formula?

Back

The difference of cubes formula states that a³ - b³ = (a - b)(a² + ab + b²).

Front

What is the sum of cubes formula?

Back

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

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, identify the greatest common factor (GCF), apply factoring techniques (like grouping, difference of squares, or special products), and continue until no further factoring is possible.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

Factor the polynomial: 27x³ + 8

Back

(3x + 2)(9x² - 6x + 4)

Front

Factor completely: 3x⁴ + 3x³ - 12x² - 12x

Back

3x(x + 2)(x - 2)(x + 1)

Front

Factor completely: 4w⁴ + 16w² + 15

Back

(2w² + 5)(2w² + 3)

Front

Factor the polynomial: 8x³ - 1

Back

(2x - 1)(4x² + 2x + 1)