Unit 2C - Factoring Flashcard Warm-Up

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 x^2 - 3x?

Back

x(x - 3)

Front

How do you factor a quadratic expression of the form ax^2 + 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. Then, rewrite the expression using these numbers to split the middle term.

Front

What is the factored form of 5x^2 + 20x + 20?

Back

5(x + 2)(x + 2) or 5(x + 2)^2.

Front

If a rectangle has an area of 4x^2 + 19x + 12 and a length of (x + 4), how do you find the width?

Back

To find the width, divide the area by the length: width = (4x^2 + 19x + 12) / (x + 4). This simplifies to (4x + 3).

Front

What is the factored form of x^2 + 11x + 24?

Back

(x + 8)(x + 3)

Front

What is the factored form of x^2 - 10x - 24?

Back

(x - 12)(x + 2)

Front

What is the significance of the zero product property in factoring?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. This is used to solve quadratic equations after factoring.

Front

What are the steps to factor a trinomial of the form x^2 + bx + c?

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to c and add to b. 3. Rewrite the expression as (x + m)(x + n), where m and n are the two numbers.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get back to the original expression.