Factoring Methods – MCQs – T4Tutorials.com

Question 1:

\[
\text{What is the factorization of } x^2 – 9?
\]
\[
\text{(a) } (x+3)(x-3), \quad \text{(b) } (x-9)(x+9), \quad \text{(c) } (x-3)^2, \quad \text{(d) } (x+9)(x-9)
\]
Answer: A

Question 2:

\[
\text{Which of the following is a factor of } x^2 – 5x + 6?
\]
\[
\text{(a) } (x-1), \quad \text{(b) } (x-2), \quad \text{(c) } (x-3), \quad \text{(d) } (x-4)
\]
Answer: B and C

Question 3:

\[
\text{The factorization of } 4x^2 – 9 \text{ is:}
\]
\[
\text{(a) } (2x-3)(2x+3), \quad \text{(b) } (4x-3)(x+3), \quad \text{(c) } (2x+9)(2x-9), \quad \text{(d) } (4x-9)(4x+9)
\]
Answer: A

Question 4:

\[
\text{What are the factors of } x^2 + 7x + 10?
\]
\[
\text{(a) } (x+2)(x+5), \quad \text{(b) } (x+1)(x+10), \quad \text{(c) } (x-2)(x+5), \quad \text{(d) } (x-1)(x+10)
\]
Answer: A

Question 5:

\[
\text{The factorization of } x^3 – 8 \text{ is:}
\]
\[
\text{(a) } (x-2)(x^2+2x+4), \quad \text{(b) } (x+2)(x^2-2x+4),
\]
\[
\text{(c) } (x+2)(x^2+2x+4), \quad \text{(d) } (x-2)(x^2-2x+4)
\]
Answer: A

Question 6:

\[
\text{Which of the following expressions cannot be factored further?}
\]
\[
\text{(a) } x^2 – 4, \quad \text{(b) } x^2 + 4, \quad \text{(c) } x^2 – 9, \quad \text{(d) } x^2 – 16
\]
Answer: B

Question 7:

\[
\text{What is the greatest common factor (GCF) of } 12x^3y^2 \text{ and } 18x^2y^3?
\]
\[
\text{(a) } 6x^2y^2, \quad \text{(b) } 12xy, \quad \text{(c) } 18x^3y^2, \quad \text{(d) } 3x^2y^2
\]
Answer: A

Question 8:

\[
\text{The factorization of } x^4 – 16 \text{ is:}
\]
\[
\text{(a) } (x^2+4)(x^2-4), \quad \text{(b) } (x+4)(x-4),
\]
\[
\text{(c) } (x^2+2)(x^2-2), \quad \text{(d) } (x+2)(x-2)(x^2+4)
\]
Answer: D

Question 9:

\[
\text{Which method is best for factoring } x^2 + 5x + 6?
\]
\[
\text{(a) } Difference of squares, \quad \text{(b) } Grouping,
\]
\[
\text{(c) } Quadratic trinomial method, \quad \text{(d) } Polynomial long division
\]
Answer: C

Question 10:

\[
\text{The factorization of } x^3 + x^2 – x – 1 \text{ is:}
\]
\[
\text{(a) } (x+1)(x^2-x-1), \quad \text{(b) } (x-1)(x^2+x-1),
\]
\[
\text{(c) } (x+1)(x^2+x+1), \quad \text{(d) } (x-1)(x^2-x+1)
\]
Answer: A

Question 11:

\[
\text{Which method is best to factor } 4x^2 – 12x + 9?
\]
\[
\text{(a) } Taking out the GCF, \quad \text{(b) } Using the AC method,
\]
\[
\text{(c) } Difference of squares, \quad \text{(d) } Completing the square
\]
Answer: B

Question 12:

\[
\text{The factorization of } 6x^2 – 7x – 5 \text{ is:}
\]
\[
\text{(a) } (2x+1)(3x-5), \quad \text{(b) } (3x+1)(2x-5),
\]
\[
\text{(c) } (2x-1)(3x+5), \quad \text{(d) } (3x-1)(2x+5)
\]
Answer: B

Question 13:

\[
\text{Which of the following is a prime polynomial?}
\]
\[
\text{(a) } x^2 – 9, \quad \text{(b) } x^2 + 3x + 2, \quad \text{(c) } x^2 + x + 1, \quad \text{(d) } x^3 – 8
\]
Answer: C

Question 14:

\[
\text{Which of the following is a perfect square trinomial?}
\]
\[
\text{(a) } x^2 + 6x + 9, \quad \text{(b) } x^2 + 5x + 6,
\]
\[
\text{(c) } x^2 – 4x + 4, \quad \text{(d) } x^2 – x + 1
\]
Answer: A and C

Question 15:

\[
\text{The factorization of } x^4 – 81 \text{ is:}
\]
\[
\text{(a) } (x^2-9)(x^2+9), \quad \text{(b) } (x-3)(x+3)(x^2+9),
\]
\[
\text{(c) } (x-3)^2(x+3)^2, \quad \text{(d) } (x^2+3x-9)(x^2-3x-9)
\]
Answer: A

More MCQs on Algebra (Collected from Past Papers)

Elementary Algebra – MCQs

Factoring Methods – MCQs
By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025