Factoring Trinomials and Verification

This video tutorial explains how to factor trinomials where the leading coefficient is not 1. It provides two examples: factoring 5n^2 + 14n + 8 and 7x^2 - 38x + 40. The video guides viewers through the process of setting up binomial factors, checking inner and outer products, and verifying the factorization by multiplying the factors back to the original expression.

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

• Multiply the terms.

• Set up the binomial factors.

• Add the coefficients.

• Find the greatest common factor.

In the trinomial 5n^2 + 14n + 8, what are the factors of the first term?

• 5n and n

• 14 and 8

• 5 and 8

• 5 and 14

Why do we only use positive factors of 8 in the trinomial 5n^2 + 14n + 8?

• Because the trinomial is positive.

• Because the middle term is positive.

• Because the first term is positive.

• Because the last term is positive.

What is the correct factorization of 5n^2 + 14n + 8?

• (5n + 2)(n + 4)

• (5n + 4)(n + 2)

• (5n + 8)(n + 1)

• (5n + 1)(n + 8)

How can you verify the factorization of a trinomial?

• By dividing the trinomial.

• By adding the factors.

• By subtracting the factors.

• By multiplying the binomials.

What is the first step in factoring the trinomial 7x^2 - 38x + 40?

• Multiply the terms.

• Find the common factor.

• Place the factors of 7x^2.

• Place the factors of 40.

Why do we use negative factors for the trinomial 7x^2 - 38x + 40?

• Because the trinomial is negative.

• Because the middle term is negative.

• Because the last term is negative.

• Because the first term is negative.

What is the correct factorization of 7x^2 - 38x + 40?

• (7x - 4)(x - 10)

• (7x - 1)(x - 40)

• (7x - 5)(x - 8)

• (7x - 10)(x - 4)

What should you avoid when placing factors into binomials?

• Using factors that are too large.

• Using positive factors.

• Using negative factors.

• Using factors that result in a common factor other than one.

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

• To ensure the sum is zero.

• To ensure the sum matches the last term.

• To ensure the sum matches the first term.

• To ensure the sum matches the middle term.