Factoring Trinomials: Techniques and Strategies

This video tutorial explains how to factor trinomials in the form of ax^2 + bx + c using the factor by grouping method. The instructor provides a detailed walkthrough of the process, including multiplying a and c, finding factor pairs, and breaking down the middle term. Several example problems are solved step-by-step, demonstrating the method's application, including cases with negative coefficients and trinomials that cannot be factored with integers. The video concludes with a summary of key points and additional practice problems.

What method is primarily used for factoring trinomials when 'a' is not 1?

• Synthetic division

• Factor by grouping

• Completing the square

• Quadratic formula

What is the first step in the factor by grouping method?

• Find the GCF of all terms

• List all factor pairs of 'c'

• Multiply 'a' and 'c'

• Rewrite the middle term as two terms

In the example with 'a' times 'c' equal to 8, which factor pair adds up to 9?

• 1 and 8

• 2 and 4

• 1 and 9

• 3 and 6

What do you do if a binomial starts with a negative term during factor by grouping?

• Multiply all terms by -1

• Ignore the negative sign

• Factor out a negative number

• Factor out a positive number

In the example with 'a' times 'c' equal to 36, which factor pair is used to split the middle term for a sum of -13?

• -4 and -9

• 4 and 9

• -3 and -12

• 3 and 12

Which factor pair of -72 adds up to positive 6?

• -6 and -12

• 6 and 12

• -8 and -9

• 8 and 9

What is the result of factoring 10x^2 + 6x - 25x - 15?

• (2x + 5)(5x + 3)

• (10x + 6)(x - 25)

• (2x - 5)(5x - 3)

• (x + 6)(x - 25)

Why is it important to check for a GCF before starting the factoring process?

• All of the above

• To identify non-factorable trinomials

• To ensure accuracy

• To simplify the trinomial

What happens if none of the factor pairs of 'ac' add up to 'b'?

• The trinomial is prime

• Use a different method

• The trinomial is non-factorable with integers

• Check for calculation errors

What is the GCF of 3a^2 + 30a + 63?

• 3

• None

• 9

• 21