Factoring Polynomials and Binomials

The video tutorial explains how to factor special cases of polynomials. It covers factoring trinomials as squares of binomials, using examples like x² + 6x + 9 and 4x² + 24x + 36. The tutorial also demonstrates factoring using the difference of squares, as seen in x² - 25, and factoring by extracting the greatest common factor (GCF) in 18x² - 50. Each example is broken down step-by-step, showing how to identify perfect squares and apply the appropriate factoring techniques.

What is the first step in factoring the trinomial x² + 6x + 9?

• Add the coefficients of the terms

• Subtract the middle term from the last term

• Multiply the first and last terms

• Identify the perfect squares of the first and last terms

How can the middle term 6x in the trinomial x² + 6x + 9 be verified?

• By adding the squares of the first and last terms

• By dividing the first term by the last term

• By doubling the product of the square roots of the first and last terms

• By subtracting the square of the last term from the first term

What is the factored form of the trinomial x² + 6x + 9?

• (x + 3)²

• (x - 3)²

• (x + 6)²

• (x - 6)²

What is the result of foiling the binomials (x + 3)(x + 3)?

• x² + 3x + 3

• x² + 9x + 9

• x² + 6x + 6

• x² + 6x + 9

In the trinomial 4x² + 24x + 36, what is the perfect square of the last term?

• 24

• 36

• 6

• 4

What is the factored form of the trinomial 4x² + 24x + 36?

• (2x + 6)²

• (2x - 6)²

• (4x + 6)²

• (4x - 6)²

How do you verify the middle term 24x in the trinomial 4x² + 24x + 36?

• By adding the squares of the first and last terms

• By dividing the first term by the last term

• By doubling the product of the square roots of the first and last terms

• By subtracting the square of the last term from the first term

What is the result of foiling the binomials (2x + 6)(2x + 6)?

• 4x² + 12x + 12

• 4x² + 24x + 36

• 4x² + 12x + 36

• 4x² + 24x + 24

What is the factored form of the binomial x² - 25?

• (x - 25)(x + 25)

• (x + 5)(x + 5)

• (x - 5)(x - 5)

• (x + 5)(x - 5)

Why is there no middle term in the binomial x² - 25?

• Because it is a difference of squares

• Because it is a sum of squares

• Because it is a perfect square trinomial

• Because it is a linear equation