Factoring flashcard

Front

What is factoring in algebra?

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 the factored form of a perfect square trinomial?

Back

The factored form of a perfect square trinomial, such as a^2 - 2ab + b^2, is (a - b)².

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor a quadratic expression of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers to group and factor.

Front

What are the steps to factor a quadratic expression completely?

Back

1. Identify the coefficients a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping. 5. Simplify if necessary.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² can be factored as (a - b)(a + b).

Front

How do you factor the expression d² - 10d + 25?

Back

The expression d² - 10d + 25 can be factored as (d - 5)(d - 5) or (d - 5)².

Front

What is the factored form of n² + 5n - 6?

Back

The factored form of n² + 5n - 6 is (n - 1)(n + 6).

Front

How do you factor the expression x² + 7x - 30?

Back

To factor x² + 7x - 30, find two numbers that multiply to -30 and add to 7, which are 10 and -3. Thus, it factors to (x + 10)(x - 3).

Front

What is the process for factoring a polynomial completely?

Back

To factor a polynomial completely, first factor out the greatest common factor (GCF), then apply techniques such as grouping, using special formulas, or trial and error for quadratics.

Front

What is the factored form of 2k² - 14k - 60?

Back

The factored form of 2k² - 14k - 60 is 2(k - 10)(k + 3).