Flashcard on Factoring (AC Method)

Front

What is the AC method in factoring?

Back

The AC method is a technique used to factor quadratic trinomials of the form ax² + bx + c by finding two numbers that multiply to ac and add to b.

Front

How do you identify the coefficients in a quadratic equation?

Back

In a quadratic equation of the form ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in factoring a quadratic using the AC method?

Back

The first step is to multiply the coefficient 'a' by the constant 'c' to find the product ac.

Front

How do you find the two numbers needed for the AC method?

Back

You need to find two numbers that multiply to ac and add to b.

Front

What do you do after finding the two numbers in the AC method?

Back

Rewrite the middle term (bx) using the two numbers found, then factor by grouping.

Front

What is factoring by grouping?

Back

Factoring by grouping involves rearranging the terms of a polynomial and grouping them in pairs to factor out common factors.

Front

Can you factor a quadratic if the leading coefficient is 1?

Back

Yes, if the leading coefficient is 1, you can factor the quadratic directly by finding two numbers that add to b and multiply to c.

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation; if it's positive, there are two distinct real roots, if zero, one real root, and if negative, no real roots.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

How do you check if your factorization is correct?

Back

You can check your factorization by multiplying the factors back together to see if you obtain the original polynomial.