Factoring Binomial Squares and Expressions

The video tutorial explains how to factor the expression -4t^2 - 12t - 9. It begins by identifying common factors and discusses the method of factoring by grouping. The tutorial then introduces the concept of binomial squares and demonstrates how to recognize and apply this pattern to simplify the factoring process. The video concludes by summarizing the methods and emphasizing the recognition of perfect square patterns.

What is the first step in factoring the expression -4t² - 12t - 9?

• Identify common factors for all terms

• Multiply all terms by 2

• Add 9 to all terms

• Divide all terms by t

Which of the following is a common factor of the first two terms in the expression?

• 3

• 4

• t

• 9

What alternative method is suggested for factoring the expression?

• Completing the square

• Using the quadratic formula

• Factoring by grouping

• Using synthetic division

What is the result of multiplying a + b by a + b?

• a² + b²

• a² - 2ab + b²

• a² + ab + b²

• a² + 2ab + b²

In the expression 4t² + 12t + 9, what is the value of 'a' if it fits the binomial square pattern?

• t

• 2t

• 3t

• 4t

What is the value of 'b' in the expression 4t² + 12t + 9 if it fits the binomial square pattern?

• 4

• 3

• 2

• 1

What is the middle term in the expression 4t² + 12t + 9 when expressed as a binomial square?

• 6t

• 4t

• 12t

• 2t

What is the factored form of 4t² + 12t + 9?

• (2t - 3)²

• (2t + 3)²

• (4t + 3)²

• (t + 3)²

What is the role of the negative 1 in the expression -4t² - 12t - 9?

• It changes the sign of the expression

• It is a common factor

• It is used to complete the square

• It is part of the binomial square

Which method might be quicker to recognize for factoring the expression?

• Completing the square

• Using the quadratic formula

• Recognizing a perfect square

• Factoring by grouping