Factoring Perfect Square Trinomials

The video tutorial explains how to factor perfect square trinomials using specific strategies. It begins with examples where the coefficient A is equal to 1, demonstrating the process of identifying perfect squares and factoring them into binomials. The tutorial then progresses to more complex examples where A is not equal to 1, emphasizing the importance of recognizing perfect squares in the first and third terms. The video concludes with a summary of the key steps and a reminder to verify the results by checking the sum of the inner and outer products.

What is the first step in factoring a perfect square trinomial when 'A' equals 1?

• Multiply the first and last terms.

• Identify the factors of the middle term.

• Find the factors of the constant term that add to the middle term.

• Divide the trinomial by the middle term.

In the example X^2 + 12X + 36, what are the factors of the trinomial?

• (X + 3)(X + 12)

• (X + 6)(X + 6)

• (X + 2)(X + 18)

• (X + 9)(X + 4)

Why is 64 considered a perfect square in the context of factoring trinomials?

• Because it is a multiple of 8.

• Because it can be expressed as 8 x 8.

• Because it is an even number.

• Because it is less than 100.

When factoring trinomials with 'A' not equal to 1, what must be true about the first and third terms?

• They must be multiples of 10.

• They must be prime numbers.

• They must be perfect squares.

• They must be even numbers.

In the trinomial 4X^2 - 12X + 9, what are the factors?

• (2X - 3)(2X - 3)

• (4X - 3)(X - 3)

• (2X + 3)(2X - 3)

• (X - 3)(X - 3)

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

• It is the product of the first and last terms.

• It determines the sign of the factors.

• It is the sum of the inner and outer products.

• It is always a perfect square.

In the example 16X^2 + 40X + 25, what are the factors?

• (4X + 5)(4X + 5)

• (4X + 5)(X + 5)

• (2X + 5)(2X + 5)

• (4X + 5)(4X - 5)

What is the purpose of checking the sum of the inner and outer products in factoring?

• To simplify the trinomial.

• To find the greatest common factor.

• To ensure the trinomial is a perfect square.

• To determine the sign of the factors.

Why is it important to recognize perfect squares in trinomials?

• To determine the sign of the factors.

• To ensure correct factorization.

• To simplify the trinomial.

• To find the greatest common factor.

What is the recommended approach to factoring perfect square trinomials?

• Guess and check.

• Factor and verify the result.

• Memorize the formula.

• Use a calculator.