Factoring when a=1

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What does it mean when a quadratic is in the form x² + bx + c?

Back

This form represents a quadratic equation where the coefficient of x² (a) is 1, making it easier to factor.

Front

How do you factor a quadratic expression like x² - 11x + 24?

Back

Look for two numbers that multiply to 24 (the constant term) and add to -11 (the coefficient of x). The factors are (x - 3)(x - 8).

Front

What is the first step in factoring a quadratic expression?

Back

Identify the coefficients of x², x, and the constant term, and determine if the expression can be factored.

Front

What are the factors of x² + 11x + 24?

Back

The factors are (x + 8)(x + 3).

Front

How do you check if your factors are correct?

Back

Multiply the factors back together to see if you get the original quadratic expression.

Front

What is the significance of the constant term in factoring?

Back

The constant term helps identify the pairs of numbers that multiply to it, which are essential for factoring.

Front

What is the relationship between the roots of a quadratic and its factors?

Back

The roots of the quadratic equation correspond to the values of x that make each factor equal to zero.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down the expression into its simplest factors, with no further factoring possible.

Front

What is the factored form of x² - 4x - 45?

Back

The factored form is (x - 9)(x + 5).