Factoring Techniques and Common Factors

The video tutorial explains how to factor trinomials in the form ax^2 + bx + c using the grouping technique, especially when 'a' is not equal to 1 and not a common factor. It provides two examples: factoring 4x^2 - 4x - 15 and 20x^2 + 19x + 3, demonstrating the step-by-step process of finding factors of 'a' times 'c' that add to 'b', rewriting the polynomial, and using grouping to factor the trinomial.

What is the first step in factoring trinomials using the grouping technique?

• Find the greatest common factor of all terms.

• Identify the factors of A x C that add to B.

• Rewrite the trinomial as a product of two binomials.

• Divide the trinomial by the leading coefficient.

In the first example, what are the correct factors of -60 that add up to -4?

• 10 and -6

• -10 and 6

• 6 and -10

• -6 and 10

What is the purpose of rewriting -4X as -10X + 6X in the first example?

• To solve the equation.

• To find the greatest common factor.

• To create four terms for grouping.

• To simplify the trinomial.

What is the greatest common factor of 4X^2 and 10X in the first example?

• 2X

• 5X

• X

• 4X

What is the final factored form of the trinomial in the first example?

• (2X - 5)(2X + 3)

• (4X - 3)(X + 5)

• (2X + 5)(2X - 3)

• (X - 5)(4X + 3)

In the second example, what is the product of A and C?

• 3

• 15

• 60

• 20

Which pair of numbers are the correct factors of 60 that add up to 19 in the second example?

• 15 and 4

• 10 and 9

• 20 and -1

• 12 and 5

What is the greatest common factor of 20X^2 and 15X in the second example?

• 5X

• 3X

• 4X

• 10X

What is the result after factoring out the common binomial factor in the second example?

• 3X + 2

• 5X + 1

• 2X - 5

• 4X + 3

What will be covered in the next video according to the conclusion?

• Applications of factoring in real-world problems.

• Another method for factoring trinomials.

• Advanced techniques in polynomial division.

• A new method for solving quadratic equations.