RASMUSSEN MAT 121 COLLEGE
ALGEBRA PRACTICE QUESTIONS
AND ANSWERS 2026/2027 – 100
MCQS WITH RATIONALES, EXAM
PREP AND STUDY GUIDE
Section 1: Algebra Fundamentals and
Linear Equations (Questions 1–15)
Question 1. Simplify the expression \(3(2x-5)+4x\).
A. \(10x-15\)
B. \(10x+15\)
C. \(6x-15\)
D. \(2x-15\)
* Answer: A. \(10x-15\)
* Rationale: Distribute 3 to obtain \(6x-15\), then combine like terms: \(6x+4x-15=10x-15\).
Question 2. Solve for \(x\): \(5x-7=18\).
A. \(3\)
B. \(4\)
C. \(5\)
D. \(7\)
* Answer: C. \(5\)
* Rationale: Add 7 to both sides to get \(5x=25\). Divide by 5 to obtain \(x=5\).
Question 3. Simplify \(x^3\cdot x^5\).
A. \(x^{15}\)
B. \(x^8\)
,C. \(x^2\)
D. \(2x^8\)
* Answer: B. \(x^8\)
* Rationale: When multiplying powers with the same base, add the exponents:
\(x^{3+5}=x^8\).
Question 4. Factor \(x^2-16\).
A. \((x-8)(x+2)\)
B. \((x-4)^2\)
C. \((x-4)(x+4)\)
D. \((x-16)(x+1)\)
* Answer: C. \((x-4)(x+4)\)
* Rationale: This is a difference of squares: \(a^2-b^2=(a-b)(a+b)\).
Question 5. Solve the inequality \(2x+3>11\).
A. \(x>4\)
B. \(x<4\)
C. \(x>7\)
D. \(x<7\)
* Answer: A. \(x>4\)
* Rationale: Subtract 3 from both sides to get \(2x>8\), then divide by 2.
Question 6. Evaluate \(2x^2-3x+1\) when \(x=2\).
A. \(1\)
B. \(3\)
C. \(5\)
D. \(7\)
* Answer: B. \(3\)
* Rationale: Substitute 2: \(2(2^2)-3(2)+1=8-6+1=3\).
, Question 7. Simplify \(\frac{x^6}{x^2}\), where \(x\ne0\).
A. \(x^3\)
B. \(x^8\)
C. \(x^4\)
D. \(x^{12}\)
* Answer: C. \(x^4\)
* Rationale: When dividing powers with the same nonzero base, subtract the exponents:
\(x^{6-2}=x^4\).
Question 8. Solve \(3(x-2)=2x+5\).
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
* Answer: C. \(11\)
* Rationale: Expand to get \(3x-6=2x+5\). Subtract \(2x\) and add 6 to find \(x=11\).
Question 9. Which expression represents the square root of \(49x^2\)?
A. \(7x\) for all real \(x\)
B. \(49x\)
C. \(7|x|\)
D. \(x+7\)
* Answer: C. \(7|x|\)
* Rationale: The principal square root is nonnegative, so \(\sqrt{49x^2}=7|x|\).
Question 10. Simplify \((2x^2)(3x^4)\).
A. \(5x^6\)
B. \(6x^8\)
C. \(6x^6\)
ALGEBRA PRACTICE QUESTIONS
AND ANSWERS 2026/2027 – 100
MCQS WITH RATIONALES, EXAM
PREP AND STUDY GUIDE
Section 1: Algebra Fundamentals and
Linear Equations (Questions 1–15)
Question 1. Simplify the expression \(3(2x-5)+4x\).
A. \(10x-15\)
B. \(10x+15\)
C. \(6x-15\)
D. \(2x-15\)
* Answer: A. \(10x-15\)
* Rationale: Distribute 3 to obtain \(6x-15\), then combine like terms: \(6x+4x-15=10x-15\).
Question 2. Solve for \(x\): \(5x-7=18\).
A. \(3\)
B. \(4\)
C. \(5\)
D. \(7\)
* Answer: C. \(5\)
* Rationale: Add 7 to both sides to get \(5x=25\). Divide by 5 to obtain \(x=5\).
Question 3. Simplify \(x^3\cdot x^5\).
A. \(x^{15}\)
B. \(x^8\)
,C. \(x^2\)
D. \(2x^8\)
* Answer: B. \(x^8\)
* Rationale: When multiplying powers with the same base, add the exponents:
\(x^{3+5}=x^8\).
Question 4. Factor \(x^2-16\).
A. \((x-8)(x+2)\)
B. \((x-4)^2\)
C. \((x-4)(x+4)\)
D. \((x-16)(x+1)\)
* Answer: C. \((x-4)(x+4)\)
* Rationale: This is a difference of squares: \(a^2-b^2=(a-b)(a+b)\).
Question 5. Solve the inequality \(2x+3>11\).
A. \(x>4\)
B. \(x<4\)
C. \(x>7\)
D. \(x<7\)
* Answer: A. \(x>4\)
* Rationale: Subtract 3 from both sides to get \(2x>8\), then divide by 2.
Question 6. Evaluate \(2x^2-3x+1\) when \(x=2\).
A. \(1\)
B. \(3\)
C. \(5\)
D. \(7\)
* Answer: B. \(3\)
* Rationale: Substitute 2: \(2(2^2)-3(2)+1=8-6+1=3\).
, Question 7. Simplify \(\frac{x^6}{x^2}\), where \(x\ne0\).
A. \(x^3\)
B. \(x^8\)
C. \(x^4\)
D. \(x^{12}\)
* Answer: C. \(x^4\)
* Rationale: When dividing powers with the same nonzero base, subtract the exponents:
\(x^{6-2}=x^4\).
Question 8. Solve \(3(x-2)=2x+5\).
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
* Answer: C. \(11\)
* Rationale: Expand to get \(3x-6=2x+5\). Subtract \(2x\) and add 6 to find \(x=11\).
Question 9. Which expression represents the square root of \(49x^2\)?
A. \(7x\) for all real \(x\)
B. \(49x\)
C. \(7|x|\)
D. \(x+7\)
* Answer: C. \(7|x|\)
* Rationale: The principal square root is nonnegative, so \(\sqrt{49x^2}=7|x|\).
Question 10. Simplify \((2x^2)(3x^4)\).
A. \(5x^6\)
B. \(6x^8\)
C. \(6x^6\)
