Simplifying Expressions and Factoring

This video tutorial focuses on simplifying rational expressions through various examples. It begins with basic examples, demonstrating how to reduce fractions by canceling common factors and using the greatest common factor (GCF). The tutorial progresses to more complex examples, including factoring trinomials and using the difference of squares technique. It also covers special cases like similar terms that require factoring out a negative one. The video concludes with practice problems and solutions, reinforcing the concepts taught.

What is the simplified form of the expression 35x^5 / 49x^2?

• 5x^3 / 7

• 7x^2 / 5

• 7x^3 / 5

• 5x^2 / 7

When simplifying 4x^2 + 8x over 3x + 6, what is the greatest common factor of the numerator?

• 8x

• 4x

• 3x

• 2x

How do you factor x^2 - 16?

• (x + 4)(x + 4)

• (x - 4)(x - 4)

• (x + 4)(x - 4)

• (x - 4)(x + 4)

What should you do when you encounter an expression like 5 - x over x - 5?

• Add 5 to both terms

• Multiply by x

• Factor out a negative one

• Cancel directly

What is the simplified form of 72x^8y^7 / 64x^5y^4?

• 8x^3y^3 / 9

• 9x^3y^3 / 8

• 9x^2y^2 / 8

• 8x^2y^2 / 9

What is the GCF of the numerator in the expression 5x^2 - 15x?

• 15

• 5x

• 15x

• 5

How do you factor the expression x^2 - 8x + 15?

• (x + 5)(x - 3)

• (x - 3)(x - 5)

• (x + 3)(x + 5)

• (x - 5)(x + 3)

What is the simplified form of 42 - 6x over 3x - 21 after factoring out the GCF?

• 2

• -2

• -3

• 3

What is the result of factoring 2x^2 - 5x - 3?

• (2x + 1)(x - 3)

• (2x - 1)(x + 3)

• (2x - 3)(x + 1)

• (2x + 3)(x - 1)

What is the simplified form of the expression x^2 - 8x + 15 over 2x^2 - 18?

• (x - 3) / (2x + 5)

• (x + 3) / (2x - 5)

• (x - 5) / (2x + 3)

• (x + 5) / (2x - 3)