Factoring Perfect Square Trinomials

The video tutorial explains how to factor the quadratic expression 25x^2 - 30x + 9. It begins by identifying that the leading coefficient is not 1 and explores the possibility of factoring by grouping. The tutorial highlights that 25 and 9 are perfect squares, suggesting the expression might be a perfect square trinomial. It then demonstrates the expansion of a binomial and matches terms to find suitable values for a and b. Finally, it shows how to factor the expression into (5x - 3)^2 or (-5x + 3)^2, explaining why both forms are equivalent.

What is the first step in factoring the expression 25x squared minus 30x plus 9?

• Use the quadratic formula

• Complete the square

• Check if it's a perfect square

• Identify common factors

Which numbers are perfect squares in the expression 25x squared minus 30x plus 9?

• 9 and 30

• 25 and 9

• 30 and 9

• 25 and 30

What is the significance of recognizing perfect squares in the expression?

• It eliminates the need for factoring by grouping

• It allows the use of the quadratic formula

• It confirms the expression is a trinomial

• It simplifies the factorization process

What is the expanded form of (ax + b) squared?

• a squared x squared + 2abx + b squared

• ax squared + bx + c

• a squared x squared + bx + c

• ax squared + 2abx + b squared

What does the term 'perfect square trinomial' imply about the expression?

• It is a quadratic equation

• It has no real roots

• It can be expressed as a binomial squared

• It has a leading coefficient of 1

If a squared is 25 and b squared is 9, what are the possible values for a and b?

• a = ±5, b = ±3

• a = ±3, b = ±5

• a = ±5, b = ±5

• a = ±3, b = ±3

What must 2ab equal to match the middle term of the expression?

• -15

• 30

• 15

• -30

What are the possible factorizations of the expression 25x squared minus 30x plus 9?

• (5x - 3) squared and (-5x + 3) squared

• (5x - 3) squared and (5x + 3) squared

• (-5x - 3) squared and (5x + 3) squared

• (5x + 3) squared and (-5x - 3) squared

Why are both factorizations of the expression equivalent?

• Because they have the same constant term

• Because they are both perfect squares

• Because they have the same coefficients

• Because negative 1 squared equals 1

How does factoring out a negative 1 affect the expression?

• It does not change the value of the expression

• It changes the sign of the constant term

• It changes the leading coefficient

• It makes the expression a perfect square