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 factor the trinomial x^2 - 5x - 24?

Back

To factor x^2 - 5x - 24, find two numbers that multiply to -24 and add to -5. The factors are (x - 8)(x + 3).

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify the coefficients a, b, and c in the trinomial ax^2 + bx + c.

Front

What is the significance of the leading coefficient in factoring?

Back

If the leading coefficient (a) is 1, the trinomial can be factored more easily into two binomials.

Front

What are the steps to factor k^2 - 2k - 24?

Back

1. Identify a, b, c. 2. Find two numbers that multiply to -24 and add to -2. 3. Write as (k + 4)(k - 6).

Front

What is the factored form of x^2 + 12x + 35?

Back

The factored form is (x + 5)(x + 7).

Front

How do you check if your factorization is correct?

Back

You can check by multiplying the binomials back together to see if you get the original trinomial.