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

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 significance of the leading coefficient being 1 in a trinomial?

Back

When the leading coefficient (a) is 1, the trinomial can be factored more easily into the form (x + p)(x + q).

Front

What is the process for factoring a trinomial when a = 1?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b.

Front

How do you factor the trinomial x^2 - 5x - 24?

Back

To factor x^2 - 5x - 24, find two numbers that multiply to -24 and add to -5, which are -8 and 3. Thus, it factors to (x - 8)(x + 3).

Front

What are the steps to factor d^2 - 10d + 25?

Back

To factor d^2 - 10d + 25, recognize it as a perfect square trinomial, which factors to (d - 5)(d - 5) or (d - 5)^2.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (a + b)^2 = a^2 + 2ab + b^2.

Front

How do you factor the trinomial x^2 + 9x + 14?

Back

To factor x^2 + 9x + 14, find two numbers that multiply to 14 and add to 9, which are 2 and 7. Thus, it factors to (x + 2)(x + 7).