Factoring Perfect Square Trinomials

The video tutorial explains how to factor perfect square trinomials by recognizing perfect squares and using specific formulas. It covers the process of checking factors through inner and outer products and discusses alternative methods for factoring trinomials. The tutorial includes examples to illustrate the concepts and emphasizes the importance of factoring out the greatest common factor first. The video concludes with a summary of the key points and additional resources for further learning.

What is a key characteristic of a perfect square trinomial?

• The first and third terms are perfect squares.

• All terms are prime numbers.

• The middle term is a perfect square.

• The trinomial has no constant term.

In the formula (A + B)^2, what does the middle term represent?

• A + B

• 2AB

• B^2

• A^2

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

• Check if the middle term is twice the product of the square roots of the first and third terms.

• Ensure all terms are even numbers.

• Check if the trinomial is a prime number.

• Verify that the trinomial is divisible by 3.

What is the result of factoring the trinomial x^2 - 10x + 25?

• (x - 10)^2

• (x + 10)^2

• (x + 5)^2

• (x - 5)^2

In the example 4x^2 - 12x + 9, what are the factors?

• (4x + 3)^2

• (2x - 3)^2

• (2x + 3)^2

• (4x - 3)^2

What is the importance of checking the inner and outer products when factoring?

• To check if the trinomial is odd

• To ensure the trinomial is a perfect square

• To confirm the trinomial is even

• To verify the trinomial is prime

When factoring a trinomial with a leading coefficient of one, what should you check for first?

• The greatest common factor

• The difference of the coefficients

• The sum of the coefficients

• The product of the coefficients

What is the first step in factoring a trinomial with a leading coefficient not equal to one?

• Use the quadratic formula

• Factor out the greatest common factor

• Divide by the leading coefficient

• Check for a perfect square trinomial

Why is it important to factor out the greatest common factor first?

• To simplify the trinomial

• To make the trinomial a perfect square

• To ensure the trinomial is prime

• To increase the degree of the trinomial

What happens if you don't factor out the greatest common factor first?

• The trinomial may not be factored completely

• The trinomial becomes a perfect square

• The trinomial is automatically simplified

• The trinomial is divided by zero