Factoring Trinomials and Grouping

This video tutorial explains how to factor a trinomial using the grouping technique when the leading coefficient is negative. It covers the process of factoring out a negative one, finding integers r and s that satisfy specific conditions, and using prime factorization to identify integer pairs. The tutorial concludes with applying the factor by grouping method to achieve the final factored form.

What is the first step in factoring a trinomial when the leading coefficient is negative?

• Factor out a negative one

• Factor out the greatest common factor

• Multiply all terms by two

• Add a constant to the trinomial

Why do we factor out a negative one from the trinomial?

• To simplify the trinomial

• To change the signs of all terms

• To make the leading coefficient positive

• To make the trinomial easier to solve

What are the integers r and s used for in the factor by grouping method?

• To find the greatest common factor

• To rewrite the trinomial in a different form

• To determine the product of a and c

• To calculate the sum of b

What is the product of a and c for the trinomial 4x^2 - 8x - 21?

• -21

• 84

• -84

• 21

Which pair of integers has a product of -84 and a sum of -8?

• (-21, 4)

• (-12, 7)

• (-14, 6)

• (-6, 14)

What is the next step after finding the integers r and s?

• Divide the trinomial by the integers

• Add the integers to the constant term

• Multiply the integers by the leading coefficient

• Factor the trinomial by grouping

What is the greatest common factor of the terms 4x^2 and -14x?

• x

• 2x

• 7x

• 4x

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

• 2x - 7

• 2x + 3

• x - 7

• x + 3

What is the final factored form of the trinomial -4x^2 + 8x + 21?

• -(2x - 7)(2x + 3)

• (2x - 7)(2x + 3)

• (2x + 7)(2x - 3)

• -(2x + 7)(2x - 3)

Why is the final factored form written with a negative sign in front?

• To simplify the expression

• To make the expression positive

• To indicate the trinomial was originally negative

• To match the original trinomial