Simplifying Expressions and Exponents

This video tutorial covers the division of polynomials by monomials. It begins with an introduction to the concept, followed by several examples that demonstrate how to simplify expressions by dividing each term in the polynomial by the monomial. The tutorial emphasizes the importance of simplifying coefficients and exponents, and it provides step-by-step solutions to ensure understanding. The video concludes with a complex example to solidify the learning objectives.

What is the first step in dividing a polynomial by a monomial?

• Divide each term in the numerator by the denominator

• Multiply each term in the numerator by the denominator

• Add the terms in the numerator

• Subtract the denominator from each term in the numerator

In the example where a = 1, b = 2, and c = 3, what is the result of (a + b) / c?

• 0

• 1

• 2

• 3

When simplifying a monomial division, what should you do with the exponents of like bases?

• Divide the exponents

• Add the exponents

• Multiply the exponents

• Subtract the exponents

How can the expression 3x/2 - 3 be alternatively expressed?

• 3/2x + 3

• 3x - 3/2

• 3/2x - 3

• 3x/2 + 3

What is the simplified form of 6x^3 / 4x?

• 3x^2/2

• x^2/2

• 3x/2

• 6x^2/4

What is the result of dividing 20a^2 by -5a^2?

• 5

• -4

• 4

• -5

How do you handle a negative exponent in the denominator?

• Leave it as is

• Move it to the numerator and change the sign

• Multiply it by the numerator

• Add it to the numerator

What is the simplified form of the expression 35a / -5a^2?

• -7a

• 7a

• -7/a

• 7/a

What is the final simplified form of the expression -4 - 7/a + 4/5a^2?

• -4 - 7a + 4/5a^2

• -4 + 7/a - 4/5a^2

• 4 - 7/a + 4/5a^2

• -4 - 7/a + 4/5a^2

What is the result of simplifying the expression 6x^2 / 4x?

• x^2/2

• 3x^2/2

• 3x/2

• x/2