Dividing and Simplifying Functions

The video tutorial explains how to find the quotients of given functions G(x) and H(x) divided by F(x). It demonstrates the process of dividing polynomials by monomials, simplifying each term individually, and ensuring positive exponents. The tutorial provides step-by-step guidance on simplifying the expressions and highlights common factors in the numerators and denominators. The video concludes with a summary of the process and encourages viewers to apply the learned techniques.

What are the functions given in the problem statement?

• A(x), B(x), and C(x)

• P(x), Q(x), and R(x)

• F(x), G(x), and H(x)

• X(x), Y(x), and Z(x)

What is the first step in dividing G(x) by F(x)?

• Multiply each term in the numerator by the denominator

• Divide each term in the numerator by the denominator

• Add each term in the numerator to the denominator

• Subtract each term in the numerator from the denominator

How do you simplify the fraction 12x^4 divided by 6x^3?

• 2

• 2x

• 2x^3

• 2x^2

What common factor is shared by 2 and 6 in the second fraction of G(x)/F(x)?

• 3

• 4

• 6

• 2

What is the expression for H(x) before division by F(x)?

• 36x^9 + 24x^6 + 2

• 12x^4 + 2

• 6x^3

• 24x^6 + 12x^4 + 2

How many fractions are formed when dividing H(x) by F(x)?

• Four

• One

• Three

• Two

What is the result of simplifying 36x^9 divided by 6x^3?

• 6x^3

• 6x^6

• 6x^2

• 6x^9

What is the simplified form of 24x^6 divided by 6x^3?

• 4x

• 4x^6

• 4x^2

• 4x^3

What is the common factor between 2 and 6 in the last term of H(x)/F(x)?

• 2

• 3

• 6

• 4

What is the final simplified form of the last term in H(x)/F(x)?

• 1/6x^3

• 1/4x^3

• 1/2x^3

• 1/3x^3