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

How do you factor the trinomial x^2 + 5x + 6?

Back

The factors are (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

What is a binomial?

Back

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

Front

How can you check if your factoring 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

The factored form is (x - 2)(x - 5) because -2 * -5 = 10 and -2 + -5 = -7.

Front

What does it mean if a trinomial cannot be factored?

Back

It means that the trinomial is either prime or does not have rational roots.