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.

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 identify the coefficients in a trinomial of the form ax^2 + bx + c?

Back

In the trinomial ax^2 + bx + c, 'a' is the coefficient of x^2, '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

When a=1, the first step is to find two numbers that multiply to 'c' and add to 'b'.

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, which are 7 and 9. Thus, it factors to (n + 7)(n + 9).

Front

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

Back

1. Identify 'b' and 'c'. 2. Find two numbers that multiply to 'c' and add to 'b'. 3. Write the factors as (x + m)(x + n), where m and n are the two numbers.

Front

What is the factored form of the trinomial m^2 - 7m + 12?

Back

The factored form is (m - 3)(m - 4).

Front

How do you check if your factorization is correct?

Back

To check if the factorization is correct, expand the factors back to see if you obtain the original trinomial.