Factoring Trinomials and Polynomials

This video tutorial explains how to factor a trinomial in two variables using the factor by grouping technique. It covers the five steps involved: finding factors of AC that add to B, rewriting the BX term, grouping terms, factoring out common factors, and finally factoring out the common binomial factor. The tutorial includes a detailed example to illustrate each step and verifies the solution by expanding the factored form back to the original expression.

What is the first step in factoring a trinomial using the grouping method?

• Identify the greatest common factor

• Find the factors of the product of the first and last coefficients that add to the middle coefficient

• Check the solution by expanding the factors

• Rewrite the trinomial as a product of binomials

In the expression 9U^2 + 3UV - 20V^2, what is the value of AC?

• 20

• 180

• -180

• -20

Why is prime factorization useful in finding the factors of AC?

• It helps in identifying pairs of factors that add to the middle term

• It simplifies the expression

• It eliminates the need for further calculations

• It directly gives the factors

Which pair of numbers multiplies to -180 and adds to 3?

• 12 and 5

• -12 and 15

• 12 and -15

• -12 and 5

How is the middle term rewritten using the factors -12 and 5?

• As 12UV - 5UV

• As 12UV + 5UV

• As -12UV - 5UV

• As -12UV + 5UV

What is the purpose of dividing the polynomial into groups?

• To check the solution

• To prepare for factoring by grouping

• To identify the greatest common factor

• To simplify the expression

What is the greatest common factor of the first group in the expression?

• 3U

• 9U

• 5V

• 4V

What is the common binomial factor in the expression after grouping?

• 3U - 5V

• 3U - 4V

• 3U + 4V

• 3U + 5V

What is the final factored form of the trinomial 9U^2 + 3UV - 20V^2?

• (3U + 4V)(3U - 5V)

• (3U - 5V)(3U + 4V)

• (3U - 4V)(3U + 5V)

• (3U + 5V)(3U - 4V)

How can you verify the factored form of a trinomial?

• By comparing with a similar trinomial

• By simplifying the expression

• By expanding the factors to see if they match the original expression

• By checking the coefficients