Factoring Trinomials and Verification

This video tutorial explains how to factor the trinomial 12x squared plus 11x minus 36. It begins by discussing the importance of identifying the greatest common factor, then moves on to setting up binomial factors. The tutorial emphasizes the need to avoid common factors in binomials and uses trial and error to find the correct factorization. The process is verified by multiplying the factors to ensure they match the original trinomial.

What is the first step in factoring any trinomial?

• Check the middle term.

• Find the greatest common factor.

• Set up the binomial factors.

• List all possible factors of the constant term.

When the leading coefficient is not 1, what should you consider first?

• The middle term.

• The sum of the inner and outer products.

• The factors of the leading coefficient.

• The factors of the constant term.

Why can't binomial factors have a common factor other than 1?

• It would make the factorization incorrect.

• It would change the middle term.

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

• It would make the trinomial unfactorable.

Why was the pair of factors negative 6 and positive 6 not considered?

• They are not factors of -36.

• They result in a positive product.

• They have a common factor other than 1.

• They do not add up to the middle term.

Which pair of factors of -36 was initially considered incorrect due to a sign issue?

• Negative 12 and positive 3

• Negative 6 and positive 6

• Negative 18 and positive 2

• Negative 9 and positive 4

What is the result of the inner product in the correct factorization?

• Negative 16x

• 11x

• 27x

• 16x

What is the result of the outer product in the correct factorization?

• 27x

• 16x

• Negative 16x

• Negative 27x

What is the correct factorization of the trinomial 12x^2 + 11x - 36?

• (12x - 3)(x + 12)

• (3x + 4)(4x - 9)

• (6x - 2)(2x + 18)

• (3x - 4)(4x + 9)

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

• To simplify the expression.

• To find the greatest common factor.

• To check if the factors are correct.

• To change the signs of the factors.

What is the final step in verifying the factorization?

• Combining like terms.

• Setting up the binomial factors.

• Listing all possible factors.

• Checking the middle term.