Chapter 9.4 Factor Trinomials (a>1) Flashcard

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 with a leading coefficient greater than 1?

Back

The first step is to multiply 'a' and 'c' (the leading coefficient and the constant term) to find the product.

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 to facilitate factoring.

Front

What is the significance of the signs in a trinomial?

Back

The signs of the terms affect the signs of the factors; a positive 'c' indicates both factors are either positive or negative.

Front

How do you check if your factors are correct after factoring?

Back

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

Front

What is the factored form of 3v² − 4v − 7?

Back

(3v − 7)(v + 1)

Front

What is the factored form of 3n² - 15n + 18?

Back

3(n - 3)(n - 2)