Factoring Trinomials when A is not 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 is not 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 is not 1?

Back

Multiply 'a' and 'c' to find the product that will help in splitting the middle term.

Front

What is the significance of the middle term in factoring?

Back

The middle term (b) is split into two terms that add up to b and multiply to ac.

Front

What is the role of the constant term in factoring?

Back

The constant term (c) helps determine the factors of the trinomial when finding pairs that multiply to ac.

Front

How do you check if your factors are correct?

Back

Multiply the binomials back together to see if you return to the original trinomial.

Front

What is a common mistake when factoring trinomials?

Back

A common mistake is forgetting to consider the signs of the factors, which can lead to incorrect products.

Front

What does it mean if a trinomial is not factorable?

Back

If a trinomial is not factorable, it cannot be expressed as a product of binomials with rational coefficients.