Factoring Trinomials (when 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 trinomial when a = 1?

Back

The standard form is x^2 + bx + c.

Front

How do you identify the coefficients in a trinomial of the form x^2 + bx + c?

Back

In the trinomial x^2 + bx + c, 'b' is the coefficient of x and 'c' is the constant term.

Front

What is the relationship between the factors of a trinomial and its roots?

Back

The factors of a trinomial correspond to the roots (or solutions) of the equation when set to zero.

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify two numbers that multiply to 'c' and add to 'b'.

Front

What is the factored form of x^2 + 5x + 6?

Back

(x + 2)(x + 3) because 2 and 3 multiply to 6 and add to 5.

Front

How can 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.

Front

What is the factored form of x^2 - 7x + 10?

Back

(x - 5)(x - 2) because -5 and -2 multiply to 10 and add to -7.

Front

What is the significance of the leading coefficient in factoring trinomials?

Back

When a = 1, the factoring process is simplified, as you only need to find two numbers that add to 'b' and multiply to 'c'.