Factoring and Solving Quadratic Equations

The video tutorial explains how to solve a quadratic equation by clearing fractions, simplifying the equation, and using factor by grouping. It begins with multiplying both sides by the least common denominator to eliminate fractions, then sets one side of the equation to zero. The trinomial is factored using grouping, and the zero product property is applied to find the solutions. The solutions are x = 5/2 and x = -2/3.

What is the first step in solving the equation with fractions?

• Add fractions to both sides

• Divide both sides by the greatest common factor

• Subtract fractions from both sides

• Multiply both sides by the least common denominator

After clearing fractions, what should be done next?

• Divide all terms by a variable

• Multiply all terms by a constant

• Add all terms to one side

• Set one side of the equation to zero

What is the result of combining like terms in the equation?

• 6x^2 - 11x + 10

• 6x^2 + 11x + 10

• 6x^2 + 11x - 10

• 6x^2 - 11x - 10

What technique is used to factor the trinomial?

• Factor by grouping

• Quadratic formula

• Completing the square

• Synthetic division

What is the product of 'a' and 'c' in the trinomial?

• 60

• -11

• -60

• 11

Which two numbers multiply to -60 and add to -11?

• -15 and 4

• 15 and -4

• -10 and 6

• 10 and -6

What is the common binomial factor in the factored equation?

• 3x + 2

• 2x - 5

• x + 1

• x - 1

What property is used to solve the factored equation?

• Commutative property

• Distributive property

• Zero product property

• Associative property

What is one of the solutions to the equation?

• x = -5/2

• x = 5/2

• x = 2/3

• x = 2/5

What is the other solution to the equation?

• x = 2/3

• x = -3/2

• x = -2/3

• x = 3/2