Factoring (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, that when multiplied together give the original expression.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the steps to factor a quadratic expression?

Back

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

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as a product of two binomials with real coefficients.

Front

What is the factored form of k^2 - 2k - 24?

Back

(k + 4)(k - 6) is the factored form of k^2 - 2k - 24.

Front

How do you determine the factors of a quadratic expression?

Back

To determine the factors, find two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of n^2 + 16n + 63?

Back

(n + 7)(n + 9) is the factored form of n^2 + 16n + 63.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the shape of the parabola and can influence the methods used for factoring, especially if a ≠ 1.

Front

What is the factored form of x^2 + 7x + 6?

Back

(x + 6)(x + 1) is the factored form of x^2 + 7x + 6.

Front

What is the factored form of x^2 - 2x - 15?

Back

(x - 5)(x + 3) is the factored form of x^2 - 2x - 15.