Back to Tutor Intake Assessment: Rewrite rational expressions

HSA.APR.D.6 Tutor Intake — Polynomial Long Division

This short check helps your tutor understand where to start with rewriting rational expressions. Answer each question on your own without help. If you are unsure, give your best try.

Grade 10·5 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-apr-d-6

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Concepts

Which of the following rational expressions is an improper rational
expression that requires polynomial long division to rewrite?

$\dfrac{x + 1}{x^2 + 3}$

$\dfrac{5}{x^2 + 1}$

$\dfrac{x^2 + 5x + 7}{x + 2}$

$\dfrac{2x - 1}{x^3 - x}$

A student divides $x^2 + 5x + 7$ by $(x + 2)$ and claims the result
is $x + 3 + \dfrac{1}{x + 2}$ .

Which check confirms this result is correct?

Substitute $x = 0$ into both $\dfrac{x^2 + 5x + 7}{x + 2}$ and
$x + 3 + \dfrac{1}{x + 2}$ and verify they give the same value.

Verify that $(x + 2)(x + 3) + 1 = x^2 + 5x + 7$ .

Verify that the degree of the remainder $1$ is less than the degree
of the divisor $(x + 2)$ .

Verify that the quotient $x + 3$ has degree one less than the
dividend $x^2 + 5x + 7$ .

Procedures

Perform polynomial long division: divide $x^2 + 5x + 7$ by $(x + 2)$ .

Enter the remainder.

Divide $x^3 - 27$ by $(x - 3)$ .

(Hint: write $x^3 - 27$ as $x^3 + 0x^2 + 0x - 27$ to handle
the missing degree terms.)

Enter the remainder.

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