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 involves rewriting it as a product of two binomials.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, 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 and affects the shape of the graph.

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial 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 process for factoring a trinomial when a=1?

Back

To factor a trinomial when a=1, find two numbers that multiply to c and add to b, then write it as (x + m)(x + n).

Front

What are the steps to check if your factorization is correct?

Back

To check if the factorization is correct, expand the binomials and see if you get the original trinomial.

Front

What is the role of the zero product property in factoring?

Back

The zero product property states that if the product of two factors is zero, at least one of the factors must be zero.

Front

How can you factor the trinomial x^2 - 7x - 44?

Back

To factor x^2 - 7x - 44, find two numbers that multiply to -44 and add to -7, which are -11 and 4. Thus, it factors to (x - 11)(x + 4).

Front

What is the factored form of z^2 + 100z + 99?

Back

The factored form of z^2 + 100z + 99 is (z + 1)(z + 99).