Factoring Special Cases

Front

What is factoring in algebra?

Back

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

Front

What is a special case in factoring?

Back

Special cases in factoring refer to specific patterns or formulas that can be used to factor certain types of polynomials, such as the difference of squares or perfect square trinomials.

Front

Factor: x² - 16

Back

(x - 4)(x + 4) - This is an example of the difference of squares.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

Factor: x² + 81

Back

Prime (not factorable) - This is an example of a sum of squares, which cannot be factored over the real numbers.

Front

Factor: x² - 25

Back

(x + 5)(x - 5) - This is another example of the difference of squares.

Front

What is a perfect square trinomial?

Back

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

Front

Factor: x² - 10x + 25

Back

(x - 5)² - This is a perfect square trinomial.

Front

What is the sum of squares?

Back

The sum of squares refers to an expression of the form a² + b², which cannot be factored over the real numbers.

Front

What is the formula for factoring a perfect square trinomial?

Back

The formula is a² ± 2ab + b² = (a ± b)².