Factoring Trinomials and Their Verification

This video tutorial explains how to factor trinomials with non-unit leading coefficients. It covers two examples: factoring 7a^2 + 18a - 40 and 3x^2 - 23x - 36. The process involves identifying factors of the constant term that, when combined with the leading coefficient, result in the middle term. The video also demonstrates how to verify the factorization by expanding the binomials back into the original trinomial.

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

• Add the coefficients of the terms.

• Set up the parentheses for binomial factors.

• Factor out the greatest common factor.

• Find the factors of the constant term.

In the first example, what are the factors of 7a^2 placed in the binomial factors?

• 7 and a

• 7a and 7

• 7a and a

• a and 7a

Which factor combination was first tried for the constant term in the first example?

• Negative 10 and positive 4

• Negative 4 and positive 10

• Negative 5 and positive 8

• Negative 8 and positive 5

What was the correct factorization for the first example?

• (7a + 10)(a - 4)

• (7a - 4)(a + 10)

• (7a - 10)(a + 4)

• (7a + 4)(a - 10)

How do you verify the factorization of a trinomial?

• By dividing the leading coefficient.

• By adding the coefficients.

• By multiplying the binomial factors.

• By subtracting the constant term.

In the second example, what are the factors of 3x^2 placed in the binomial factors?

• 3x and 3

• 3x and x

• 3 and x

• x and 3x

Which factor combination was used to achieve the correct factorization in the second example?

• Negative 6 and positive 6

• Negative 9 and positive 4

• Negative 4 and positive 9

• Negative 3 and positive 12

What is the correct factorization for the second example?

• (3x - 4)(x + 9)

• (3x + 4)(x - 9)

• (3x - 9)(x + 4)

• (3x + 9)(x - 4)

What is the sum of the inner and outer products in the correct factorization of the second example?

• Negative 36x

• Positive 36x

• Positive 23x

• Negative 23x

What is the purpose of listing factor combinations in trinomial factorization?

• To find the greatest common factor.

• To eliminate the constant term.

• To determine the sum of the inner and outer products.

• To simplify the trinomial.