Factoring Difficult Trinomials

The video tutorial explains how to factor difficult trinomials using the quadratic formula. It begins by introducing the problem of factoring complex trinomials and then demonstrates how to apply the quadratic formula to find solutions. The tutorial walks through solving the quadratic equation step-by-step, finding the factors, and verifying the factored expression. The video concludes by summarizing the process and emphasizing the usefulness of the quadratic formula for factoring challenging trinomials.

What is the first step in factoring a difficult trinomial like 12x² + 243x - 189?

• Find two numbers that multiply to the constant term.

• Use the quadratic formula.

• Multiply the leading coefficient by the constant term.

• Add the coefficients together.

What is the value of b in the quadratic formula for the trinomial 12x² + 243x - 189?

• 12

• 243

• 189

• 2268

What is the result of 243 squared in the quadratic formula?

• 59049

• 261

• 9072

• 2268

What are the two roots obtained from the quadratic formula for the trinomial 12x² + 243x - 189?

• 2/3 and -20

• 5/6 and -19

• 1/2 and -18

• 3/4 and -21

How do you derive the factor x + 21 from the root -21?

• Add 21 to both sides of the equation.

• Subtract 21 from both sides of the equation.

• Multiply both sides by 21.

• Divide both sides by 21.

What is the factor derived from the root 3/4?

• x - 3/4

• x + 3/4

• 4x - 3

• 4x + 3

What is the purpose of adding a 3 to the expression 4x times x?

• To make it equal to 12x².

• To simplify the expression.

• To factor out the greatest common factor.

• To eliminate the constant term.

What is the result of distributing 3 in the expression 3(4x - 3)?

• 12x + 9

• 12x - 9

• 4x - 9

• 4x + 9

What is the result of multiplying 12x by 21 in the verification process?

• 261x

• 189x

• 252x

• 243x

What is the final step in verifying the factored expression?

• Divide the two middle terms.

• Multiply the two middle terms.

• Subtract the two middle terms.

• Add the two middle terms together.