Factoring Trinomials and Binomials

This video tutorial explains how to factor trinomials where the leading coefficient is not 1. It provides two examples: 6P^2 + 7P - 20 and 8x^2 - 42x + 27. The process involves setting up binomial factors, using trial and error to find the correct factors, and verifying the results by expanding the binomials back into the original trinomial. The tutorial emphasizes the importance of ensuring no common factors exist in the binomials unless present in the original trinomial.

What is the first step in factoring a trinomial where the leading coefficient is not 1?

• List all possible factors of the middle term.

• Divide the trinomial by the leading coefficient.

• Multiply the first and last coefficients.

• Factor out the greatest common factor.

In the first example, what are the possible pairs of factors for 6P^2?

• 3P and 2P, 6P and P

• 2P and 3P, 4P and 1.5P

• 6P and 1P, 3P and 3P

• 4P and 1.5P, 2P and 3P

Why should none of the binomial factors have a common factor other than 1?

• It ensures the factors are unique.

• It helps in finding the correct factors quickly.

• It makes the factorization process easier.

• It would indicate a common factor in the original trinomial.

What is the correct factorization of 6P^2 + 7P - 20?

• (2P - 4)(3P + 5)

• (3P + 4)(2P - 5)

• (3P - 4)(2P + 5)

• (2P + 4)(3P - 5)

What is the purpose of verifying the factorization by expanding the binomials?

• To check for errors in the coefficients.

• To simplify the trinomial further.

• To find new factors.

• To ensure the original trinomial is obtained.

In the second example, what are the possible pairs of factors for 8x^2?

• 5x and 1.6x, 2x and 4x

• 4x and 2x, 8x and x

• 2x and 4x, 6x and 1.5x

• 8x and 1x, 3x and 3x

Why are negative factors used for the constant term in the second example?

• To simplify the trinomial.

• To ensure the factors are unique.

• To make the factorization process faster.

• Because the sum of the products must be negative.

What is the correct factorization of 8x^2 - 42x + 27?

• (4x - 3)(2x - 9)

• (2x + 3)(4x + 9)

• (4x + 3)(2x + 9)

• (2x - 3)(4x - 9)

What is the result of expanding the binomials (4x - 3)(2x - 9)?

• 8x^2 - 42x + 27

• 8x^2 + 42x - 27

• 8x^2 - 36x + 27

• 8x^2 + 36x - 27

Why is it important to verify the factorization by expanding the binomials?

• To check for errors in the middle term.

• To find additional factors.

• To simplify the expression.

• To confirm the factorization is correct.