Factoring Trinomials (a = 1)

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial means rewriting it as a product of two binomials.

Front

What is the standard form of a trinomial?

Back

The standard form of a trinomial is ax^2 + bx + c, where a, b, and c are constants.

Front

What is the first step in factoring a trinomial when a = 1?

Back

Identify two numbers that multiply to c and add to b.

Front

Factor the trinomial: x^2 - 5x + 6

Back

(x - 2)(x - 3)

Front

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

Back

The roots of a trinomial are the values of x that make the trinomial equal to zero, and they correspond to the factors.

Front

How do you check if your factorization is correct?

Back

Multiply the factors back together to see if you get the original trinomial.

Front

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

Back

The leading coefficient (a) affects the shape and direction of the parabola represented by the trinomial.

Front

What are the possible signs of the factors of a trinomial?

Back

The signs of the factors depend on the signs of b and c in the trinomial.

Front

What is the factored form of x^2 + 4x + 4?

Back

(x + 2)(x + 2) or (x + 2)^2.