Factoring

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 quadratic expression?

Back

The factored form of a quadratic expression ax² + bx + c is typically expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a - b)(a + b).

Front

What is the factored form of x² - 25?

Back

(x - 5)(x + 5) is the factored form of x² - 25.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are those two numbers.

Front

What is the area of a rectangle formula?

Back

The area of a rectangle is calculated using the formula Area = length × width.

Front

How do you find the width of a rectangle if the area and length are known?

Back

To find the width, divide the area by the length: Width = Area / Length.

Front

What is the factored form of 2x² - 3x - 2?

Back

(2x + 1)(x - 2) is the factored form of 2x² - 3x - 2.

Front

What is the significance of the coefficients in a quadratic expression?

Back

The coefficients in a quadratic expression determine the shape and position of the parabola represented by the equation.

Front

How do you factor the expression 80x² + 15x?

Back

First, factor out the greatest common factor (GCF), which is 5x, resulting in 5x(16x + 3).