Factoring Trinomials when a = 1 AND a >1

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + 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 when a = 1?

Back

When a = 1, the trinomial can be factored as (x + p)(x + q) where p and q are numbers that add to b and multiply to c.

Front

How do you identify p and q in the trinomial x^2 + bx + c?

Back

p and q are the two numbers that add up to b (the coefficient of x) and multiply to c (the constant term).

Front

Factor the trinomial: x^2 + 5x + 6.

Back

(x + 2)(x + 3)

Front

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

Back

When a > 1, the trinomial can be factored as a(x + p)(x + q) where p and q are found similarly.

Front

How do you factor a trinomial when a > 1?

Back

1. Multiply a and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

Factor the trinomial: 2x^2 + 7x + 3.

Back

(2x + 1)(x + 3)

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the method of factoring, especially when a > 1.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, typically in the form (x + p)(x + q).