Warm Up: Factoring (use before Simplifying Rational Expressions)

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 difference between factoring completely and factoring partially?

Back

Factoring completely means breaking down an expression into its simplest factors, while factoring partially means finding some factors but not all.

Front

What is the factored form of a difference of squares?

Back

The factored form of a difference of squares, a^2 - b^2, is (a + b)(a - b).

Front

How do you factor a quadratic expression of the form ax^2 + bx + c?

Back

To factor a quadratic expression of the form ax^2 + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

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

Back

The factored form is 2(k - 10)(k + 3).

Front

What are the steps to factor a trinomial?

Back

1. Identify a, b, and c from ax^2 + bx + c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

What is the factored form of k^2 + 7k + 10?

Back

The factored form is (k + 2)(k + 5).

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient affects the methods used for factoring, especially in determining the possible rational roots and the overall structure of the factors.

Front

How do you factor the expression 3v^2 - 4v - 7?

Back

The factored form is (3v - 7)(v + 1).

Front

What is the factored form of the expression 3x^2 + 18x + 15?

Back

The factored form is 3(x + 5)(x + 1).