8.2 Factoring Trinomials ( a =1)

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of 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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the relationship between the coefficients and the roots of a trinomial?

Back

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a.

Front

How do you factor the trinomial n^2 + 16n + 63?

Back

To factor n^2 + 16n + 63, find two numbers that multiply to 63 and add to 16. The factors are (n + 7)(n + 9).

Front

What are the steps to factor a trinomial of the form x^2 + bx + c?

Back

1. Identify two numbers that multiply to c and add to b. 2. Rewrite the trinomial as (x + m)(x + n), where m and n are the identified numbers.

Front

What is the factored form of k^2 - 2k - 24?

Back

The factored form is (k + 4)(k - 6).

Front

How can you check if your factorization is correct?

Back

You can check by expanding the factors back to the original trinomial.

Front

What is the factored form of x^2 - 8x + 15?

Back

The factored form is (x - 5)(x - 3).

Front

What is the significance of the leading coefficient in a trinomial?

Back

In the case of a = 1, the trinomial can be factored more easily as it simplifies the process.