Factoring Trinomials where a >1

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the general form of factoring a trinomial where a > 1?

Back

The general form is ax² + bx + c = (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In 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 trinomial where a > 1?

Back

Multiply 'a' and 'c' to find the product ac.

Front

What is the purpose of finding two numbers that multiply to ac and add to b?

Back

These two numbers help in splitting the middle term (bx) for easier factoring.

Front

How do you split the middle term in a trinomial?

Back

Rewrite bx as the sum of two terms using the two numbers found that multiply to ac and add to b.

Front

What is the next step after splitting the middle term?

Back

Group the terms into two pairs and factor out the common factors from each pair.

Front

What do you do after factoring out common factors from each pair?

Back

Factor out the common binomial from the two groups.

Front

What is the factored form of 2x² + 3x - 9?

Back

(x + 3)(2x - 3)