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 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) because 2 * 3 = 6 and 2 + 3 = 5.

Front

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

Back

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

Front

How do you check if your factorization is correct?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial that consists of two terms, typically in the form ax + b.

Front

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

Back

The leading coefficient (a) determines the degree and direction of the parabola represented by the trinomial.

Front

What does it mean if a trinomial cannot be factored?

Back

It means that the trinomial does not have rational roots and cannot be expressed as a product of binomials.