Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that divides two or more numbers or expressions.

Front

How do you factor the expression x² - 10x + 24?

Back

To factor x² - 10x + 24, find two numbers that multiply to 24 and add to -10. The factors are (x - 6)(x - 4).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

Front

Can the expression 9n² + 1 be factored?

Back

No, 9n² + 1 cannot be factored using the difference of squares or other common methods.

Front

What is the first step in factoring the expression 2c² + 2c - 84?

Back

The first step is to factor out the greatest common factor, which is 2, resulting in 2(c² + c - 42).

Front

What are the steps to factor a quadratic expression?

Back

1. Write the expression in standard form. 2. Identify a, b, and c. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the expression using these numbers. 5. Factor by grouping if necessary.

Front

What is the factored form of 4a² - 25?

Back

The factored form of 4a² - 25 is (2a + 5)(2a - 5), using the difference of squares.

Front

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

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.