Factoring (warm up)

Front

What is factoring?

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 sum of cubes?

Back

A sum of cubes is an expression of the form a³ + b³, which can be factored using the formula: a³ + b³ = (a + b)(a² - ab + b²).

Front

What is a difference of cubes?

Back

A difference of cubes is an expression of the form a³ - b³, which can be factored using the formula: a³ - b³ = (a - b)(a² + ab + b²).

Front

Factor the expression: 2x³ + 128

Back

2(x + 4)(x² - 4x + 16)

Front

Factor the expression: x³ + 1

Back

(x + 1)(x² - x + 1)

Front

Factor the expression: x³ - 343

Back

(x - 7)(x² + 7x + 49)

Front

What is the formula for factoring a sum of cubes?

Back

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

Front

What is the formula for factoring a difference of cubes?

Back

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

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all terms of the polynomial.

Front

How do you factor x³ + 1 using the sum of cubes formula?

Back

Identify a = x and b = 1, then apply the formula: (x + 1)(x² - x + 1).