Factoring and Solving Quadratic Equations

The video tutorial covers solving rational equations by eliminating fractions and factoring. It demonstrates how to factor trinomials and identify values that make the function undefined. The tutorial also explains the process of cross-multiplying to solve equations, providing step-by-step guidance on each method. The video concludes with identifying correct solutions and eliminating incorrect ones based on the context of the problem.

What is the first step recommended to solve the rational equation 10/(x-2) = x + 1?

• Subtract x from both sides

• Divide by 10

• Multiply everything by x

• Add 2 to both sides

After eliminating the fraction, what is the resulting equation before combining like terms?

• x^2 + x = 10

• x^2 - 2x = 10

• 10 = x^2 + x - 2x

• x^2 + 3x - 10 = 0

Which two numbers multiply to -10 and add to 3 in the trinomial x^2 + 3x - 10?

• 10 and -1

• 5 and -2

• -5 and 2

• 3 and -3

What is the correct factorization of x^2 + 3x - 10?

• (x - 2)(x + 5)

• (x + 2)(x - 5)

• (x - 5)(x + 2)

• (x + 5)(x - 2)

What are the two solutions obtained after factoring x^2 + 3x - 10?

• x = -5 and x = -2

• x = 5 and x = 2

• x = -5 and x = 2

• x = 5 and x = -2

Which two numbers multiply to -24 and add to -2 in the trinomial x^2 - 2x - 24?

• -6 and 4

• -8 and 3

• 8 and -3

• 6 and -4

What x-values make the denominator zero in the equation with trinomials?

• x = -3, x = 4, x = -2

• x = 3, x = 4, x = 2

• x = 3, x = -4, x = -2

• x = -3, x = -4, x = 2

What is the next step after simplifying the equation to x - 6 = 12/(x - 2)?

• Divide by x

• Subtract 12 from both sides

• Cross-multiply

• Add 6 to both sides

What is the greatest common factor (GCF) used to factor x^2 - 8x?

• 8

• x

• x - 8

• 2x

What is the correct solution for x after factoring x(x - 8) = 0?

• x = 8 and x = -8

• x = 0 and x = -8

• x = 0 and x = 8

• x = 0 and x = 0