Skills Review for Antiderivatives

Learning Outcomes

  • Divide polynomials by monomials
  • Write function equations using given conditions

In the Antiderivatives section, we will sometimes simplify rational expressions by dividing a polynomial in the numerator by a monomial in the denominator.

Divide a Polynomial by a Monomial

When dividing a polynomial by a monomial, it is important that every term of the polynomial is divided by the monomial. You will then want to simplify. Here we will review this topic.

Example: Dividing a Polynomial by a Monomial

Perform each division. Be sure to simplify your answer.

  1. [latex]\dfrac{9{x}^{3}+6x}{3{x}^{2}}[/latex]
  2. [latex]\dfrac{{x}^{9}+3{x}^{6}}{{x}^{4}}[/latex]

Try It

Write Function Equations Using Given Conditions

Sometimes, to find a missing value in a function equation, you will be given an input of the function and the corresponding output. You will then plug this input and output into the function equation and find the missing value.

Example: Writing a Function Equation from given conditions

Given [latex]f(2)=-1[/latex], find the unknown value c in the function equation [latex]f(x)=3x^3-4x^2-x+c[/latex].

 

Try It

Given [latex]f(1)=5[/latex], find the unknown value c in the function equation [latex]f(x)=-2x^2+3x+c[/latex].