Flashcard 0.5 - Factoring Perfect Square Trinomials & Grouping

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be written in the form (a + b)² or (a - b)², which expands to a² ± 2ab + b².

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

Factor the perfect square trinomial: n² + 10n + 25.

Back

(n + 5)².

Front

Factor the perfect square trinomial: x² - 24x + 144.

Back

(x - 12)².

Front

Factor the perfect square trinomial: x² + 18x + 81.

Back

(x + 9)².

Front

What is the formula for factoring a perfect square trinomial?

Back

The formula is a² ± 2ab + b² = (a ± b)².

Front

What are the steps to factor a perfect square trinomial?

Back

1. Identify a² and b². 2. Check if the middle term is ±2ab. 3. Write the expression as (a ± b)².

Front

What is the significance of the middle term in a perfect square trinomial?

Back

The middle term must equal ±2 times the product of the square roots of the first and last terms for the trinomial to be a perfect square.

Front

Can a trinomial be factored if it is not a perfect square?

Back

Yes, trinomials can often be factored using other methods, such as grouping or the quadratic formula.

Front

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

Back

A perfect square trinomial can be expressed as the square of a binomial, while a regular trinomial may not have this property.