Factoring Quadratics

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials, if possible, or identifying common factors.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a ± b)², where a² ± 2ab + b² is the trinomial.

Front

What is the greatest common factor (GCF) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in an expression. It is used to factor out common terms from polynomials.

Front

What is the factored form of the expression 4x² - 20x + 25?

Back

The factored form is (2x - 5)².

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 factored form is (x - 6)(x - 4).

Front

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

Back

The coefficients a, b, and c in ax² + bx + c determine the shape and position of the parabola represented by the quadratic function.

Front

What is the factored form of the expression 24c⁵ - 12c³?

Back

The factored form is 12c³(2c² - 1).

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as a + b or x² - 4.