Example 3: Factoring quadratics as a perfect square of a sum: (a+b)^2 | Algebra I | Khan Academy

TL;DR

The video explains how to factor a perfect square trinomial and identifies the pattern to recognize it.

Transcript

We need to factor negative 4t squared minus 12t minus 9. And a good place to start is to say, well, are there any common factors for all of these terms? When you look at them, well these first two are divisible by 4, these last 2 are divisible by 3, but not all of them are divisible any one number. Will, but you could factor out a negative 1, but e... Read More

Key Insights

• 🧑‍🏭 The trinomial -4t^2 - 12t - 9 can be factored as (-1)(2t + 3)^2, where (-1) is factored out and 2t + 3 is the perfect square binomial.
• 💯 Recognizing the pattern of a perfect square binomial can expedite the factoring process.
• 😑 Factoring a perfect square trinomial simplifies the expression and makes solving quadratic equations more manageable.
• ❎ The constant term in a perfect square trinomial can be positive or negative, depending on the square root of the last term.

Questions & Answers

Q: How do you determine if a trinomial is a perfect square?

To determine if a trinomial is a perfect square, you need to check if the first term is a square, the last term is a square, and the middle term is twice the product of the square roots of the first and last terms.

Q: What is the pattern of a perfect square binomial?

The pattern of a perfect square binomial is (a + b)^2 = a^2 + 2ab + b^2, where a is the square root of the first term and b is the square root of the last term.

Q: Can the constant term in a perfect square trinomial be negative?

Yes, the constant term in a perfect square trinomial can be negative. It can be either the positive or negative square root of the last term.

Q: Why is factoring a perfect square trinomial useful?

Factoring a perfect square trinomial allows you to simplify expressions and solve quadratic equations more easily. It helps identify a known pattern and allows for quicker calculations.

Summary & Key Takeaways

• The content discusses factoring the trinomial -4t^2 - 12t - 9 and explores if it has any common factors.

• The video demonstrates that the trinomial can be factored as (-1)(2t + 3)^2.

• The content shows that the trinomial fits the pattern of a perfect square binomial and provides an alternative method to factor it.