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 involves rewriting it as a product of two binomials.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The leading coefficient (a) determines the direction of the parabola when graphed.

Front

How do you identify the coefficients in a trinomial?

Back

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

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 + 4

Back

(x + 4)(x + 1)

Front

Factor the trinomial: x^2 - 9x + 20

Back

(x - 5)(x - 4)

Front

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

Back

The roots of the trinomial are the values of x that make each factor equal to zero.

Front

How can you check if your factorization is correct?

Back

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