Factoring Trinomials a > 1

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of 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

What is the first step in factoring a trinomial with a leading coefficient greater than 1?

Back

The first step is to multiply the leading coefficient (a) by the constant term (c).

Front

How do you find two numbers that multiply to ac and add to b?

Back

You need to find two integers that multiply to the product of the leading coefficient and the constant term (ac) and add up to the middle coefficient (b).

Front

What is the significance of the signs in the factors of a trinomial?

Back

The signs of the factors depend on the signs of the constant term and the middle term; they help determine how to split the middle term.

Front

What is the role of the 'box method' in factoring trinomials?

Back

The box method is a visual aid that helps organize the terms of the trinomial and find the factors systematically.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into its multiplicative components, while expanding is multiplying out the factors to get the original expression.

Front

What is a common mistake when factoring trinomials?

Back

A common mistake is failing to check if the factors multiply back to the original trinomial.

Front

How can you verify that your factors are correct?

Back

You can verify by multiplying the factors back together to see if you obtain the original trinomial.