SAT Polynomial / Rational Expressions

Polynomial and rational expression questions test factoring, dividing and simplifying — including what remains after a cancellation. Cancelling correctly and then failing to combine what is left is the trap the bank names for this skill.

Practise this skill freeHow the SAT is structured
MathAdvanced Math112 questions
The trap on this skill

Cancelling correctly but forgetting to combine the remaining x-term with the added term.

How this skill behaves

What 112 questions on it look like

89% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

44% of the bank for this skill is rated hard, so it rewards practice past the point where the basic form feels comfortable.

medium46%
hard44%
easy11%

Difficulty mix across the 112 questions in this skill.

From the bank

Three real polynomial / rational expressions questions

Each one explains the credited answer and why every other option fails.

Advanced Math · hard

In a simplification used for the rooftop evening mural plotting layout note, x cannot equal 7. Which expression is equivalent to (x^2 - 49)/(x - 7) + 4x?

  1. A5x - 7
  2. B5x + 7correct
  3. C4x + 7
  4. Dx + 7
Why B is correct — and why the others are not

Factor x^2 - 49 as (x - 7)(x + 7). After canceling x - 7, the expression becomes x + 7 + 4x = 5x + 7. The key support is the way the item treats Polynomial / rational expressions. A final check is using the midpoint, area, or angle relationship explicitly.

A. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

C. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

D. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

Advanced Math · medium

In a simplification used for the makerspace weekday sign mixing count sheet, x cannot equal 4. Which expression is equivalent to (x^2 - 16)/(x - 4) + 5x?

  1. A6x - 4
  2. B5x + 4
  3. C6x + 4correct
  4. Dx + 4
Why C is correct — and why the others are not

Factor x^2 - 16 as (x - 4)(x + 4). After canceling x - 4, the expression becomes x + 4 + 5x = 6x + 4. This is the only choice that stays consistent with the detail about Polynomial / rational expressions. A final check is checking whether a calculator result answers the actual question.

A. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

B. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

D. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

Advanced Math · easy

In a simplification used for the conservatory quiet panel staging receipt, x cannot equal 3. Which expression is equivalent to (x^2 - 9)/(x - 3) + 5x?

  1. A6x - 3
  2. B5x + 3
  3. C6x + 3correct
  4. Dx + 3
Why C is correct — and why the others are not

Factor x^2 - 9 as (x - 3)(x + 3). After canceling x - 3, the expression becomes x + 3 + 5x = 6x + 3. This is the only choice that stays consistent with the detail about Polynomial / rational expressions. A final check is testing the value in the original relationship.

A. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

B. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

D. This value results from cancelling correctly but forgetting to combine the remaining x-term with the added term

112 questions on this skill, free to start.

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FAQ

Polynomial / Rational Expressions questions

How do I simplify a rational expression?

Factor numerator and denominator fully, cancel common factors, then combine whatever remains. The last step is the one people skip.

Do I need polynomial long division?

Occasionally. More often factoring is enough, and looking for a common factor first saves the division.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Quadratic Functions and Equations135 questionsNonlinear Equations in One Variable127 questionsEquivalent Expressions120 questionsExponential Functions and Equations113 questions

Practise polynomial / rational expressions until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

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