Factoring Review

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

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms, divide each term by the GCF, and express the original expression as the product of the GCF and the resulting expression.

Front

What is the difference of squares formula?

Back

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

Front

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

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers to split the middle term, then factor by grouping.

Front

What is the factored form of x² - 49?

Back

The factored form is (x + 7)(x - 7), which is derived using the difference of squares formula.

Front

What is the factored form of 5n² - 6n - 27?

Back

The factored form is (5n - 9)(n + 3), found by identifying two numbers that multiply to -135 (5 * -27) and add to -6.

Front

How do you factor a trinomial of the form k² + bx + c?

Back

To factor a trinomial, find two numbers that multiply to c and add to b. Rewrite the trinomial as a product of two binomials.

Front

What is the factored form of k² + 7k + 10?

Back

The factored form is (k + 2)(k + 5), derived by finding two numbers that multiply to 10 and add to 7.

Front

What is the factored form of 9x² - 49?

Back

The factored form is (3x + 7)(3x - 7), which is derived using the difference of squares formula.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging terms in a polynomial, grouping them into pairs, and factoring out the common factors from each group.