Factoring Quadratics with leading coefficients

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, 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 involves rewriting it as a product of two binomials.

Front

What is the standard form of a quadratic expression?

Back

The standard form of a quadratic expression is ax^2 + bx + c.

Front

What is the leading coefficient in a quadratic expression?

Back

The leading coefficient is the coefficient of the term with the highest degree, which is 'a' in the expression ax^2 + bx + c.

Front

How do you identify the factors of a quadratic expression?

Back

To identify the factors, look for two numbers that multiply to give ac (the product of a and c) and add to give b.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor it into simpler expressions.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What are the steps to factor a quadratic expression of the form ax^2 + bx + c?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms.

Front

What is the FOIL method in relation to binomials?

Back

The FOIL method is a technique for multiplying two binomials, standing for First, Outside, Inside, Last.