Factoring Trinomials (when 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 when 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 when a > 1?

Back

Multiply 'a' and 'c' to find the product that will help in finding two numbers that add to 'b'.

Front

What is the significance of the two numbers found when factoring?

Back

The two numbers must add up to 'b' and multiply to 'ac'.

Front

How do you set up the binomials after finding the two numbers?

Back

Use the two numbers to split the middle term and rewrite the trinomial as two binomials.

Front

What is the role of the leading coefficient in factoring?

Back

The leading coefficient affects how you group the terms when factoring.

Front

Can all trinomials be factored?

Back

Not all trinomials can be factored; some are prime and cannot be expressed as a product of binomials.

Front

What is a prime trinomial?

Back

A prime trinomial is one that cannot be factored into simpler binomials.