Factoring Trinomials a=1

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + 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 ax² + 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 when graphed and affects the factoring process.

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial ax² + bx + c, 'a' is the coefficient of x², '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

When a = 1, you look for two numbers that multiply to c and add to b, then write the factors as (x + m)(x + n).

Front

What are the steps to factor a trinomial with a leading coefficient greater than 1?

Back

1. Multiply a and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

What is the difference between a perfect square trinomial and a regular trinomial?

Back

A perfect square trinomial can be factored into the square of a binomial, while a regular trinomial cannot.

Front

How can you recognize a perfect square trinomial?

Back

A trinomial is a perfect square if it can be expressed as (a ± b)², which expands to a² ± 2ab + b².

Front

What is the factored form of d² - 10d + 25?

Back

(d - 5)(d - 5) or (d - 5)².