Factoring and Simplifying Expressions

This video tutorial teaches how to find missing dimensions in geometric problems by rewriting rational expressions. It covers factoring and long division techniques to simplify expressions and solve for unknown dimensions like width, height, and length in rectangles and prisms. The tutorial reviews previous lessons on rational expressions and demonstrates practical applications in calculating area and volume.

What is the width of a rectangle with an area of 28x² + x - 13 and a length of 4x + 3?

• x - 2

• 7x - 5

• 4x + 3

• 2x + 1

Which method is used to simplify common factors in rational expressions?

• Addition

• Factoring

• Multiplication

• Long division

When using long division, what should you remember to distribute?

• Only the constant term

• All terms in the divisor

• Only the first term

• Only the last term

What is the importance of distributing the term times all terms in the divisor?

• To find the greatest common factor

• To correctly perform long division

• To simplify the expression

• To ensure the remainder is zero

What is the product of 4x + 3 and 7x - 5?

• 28x² + 2x - 15

• 28x² + x - 15

• 28x² + x - 13

• 28x² + 3x - 15

What is the width of a rectangle if the expression is simplified to 7x - 5 plus 2 over 4x + 3?

• 2x + 1

• 7x - 5 + 2/(4x + 3)

• 4x + 3

• 7x - 5

How do you find the height of a square-based prism if the length and width are the same?

• Divide the product of width and height by the width

• Subtract the width from the length

• Divide the volume by the length

• Multiply the length by the width

What is the result of dividing the volume by the height in a rectangular prism?

• The length

• The width

• The height

• The product of the length and width

What is the factored form of x² + 2x - 35?

• (x + 5)(x - 7)

• (x + 3)(x - 12)

• (x + 6)(x - 6)

• (x + 7)(x - 5)

What is the process to find the missing dimensions in area or volume problems?

• Using addition

• Rewriting rational expressions

• Using multiplication

• Using subtraction