Q1. LCM of 4x²y and 8x³y² is:
The LCM takes the highest powers of all prime factors: 8, x³, and y².
Class 9 Math Chapter 4: Factorization and Algebraic Manipulation MCQs With Explanations
Practice Class 9 Math Chapter 4: Factorization and Algebraic Manipulation MCQs with explanations for Pakistani board exams. Includes solved objective questions, answer checking, chapter revision guidance and next chapter suggestions.
15 MCQs
Chapter 4: Factorization and Algebraic Manipulation Objective Preparation
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15Total MCQs
15With explanations
3Topics represented
Topics found: HCF and LCM, Factorization, Polynomials
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Factorization and Algebraic Manipulation MCQs With Explanations
Q2. HCF of 6x³ – 17x² – 5x + 6 and 6x³ – 5x² – 3x + 2 is:
The HCF of the two cubics is 6x² + x – 2, as it is the common polynomial factor after factoring both expressions.
Q3. HCF of 6x²y and 9xy² is:
The HCF is the product of the lowest powers of common factors: 3, x, and y.
Q4. The factors of x² - 11x + 24 are:
The quadratic x² - 11x + 24 factors as (x - 8)(x - 3) because -8 and -3 multiply to +24 and add to -11.
Q5. The factors of x² + 9x + 14 are:
x² + 9x + 14 factors as (x + 2)(x + 7) because 2 and 7 multiply to 14 and add to 9.
Q6. The factors of x² – 3x – 10 are:
x² – 3x – 10 factors as (x + 2)(x – 5) because 2 and –5 multiply to –10 and add to –3.
Q7. One of the factors of x³ – 27 is:
x³ – 27 = (x – 3)(x² + 3x + 9), so both (x – 3) and (x² – 3x + 9) are factors? Wait — correction needed.
Q8. Cubic polynomial has degree:
A cubic polynomial is defined by its highest degree term being 3.
Q9. Factorization of x³ + 3x² + 3x + 1 is:
The expression matches the expansion of (x + 1)³ = x³ + 3x² + 3x + 1.
Q10. The LCM of (a – b)² and (a – b)⁴ is:
LCM takes the highest power of the common base: (a – b)⁴ is the highest power present.
Q11. Product of LCM and HCF = _______ of two polynomials:
For any two polynomials, the product of their LCM and HCF equals the product of the polynomials themselves.
Q12. The LCM of 16x², 4x and 30xy is:
LCM takes highest powers: 240 (LCM of 16,4,30), x² (highest power of x), and y (from 30xy).
Q13. The HCF of a³b³ and ab² is:
The HCF is the lowest power of common variables: a¹ and b², so ab².
Q14. The factors of 4x² – 12x + 9 are:
The expression 4x² – 12x + 9 is a perfect square trinomial: (2x)² – 2·2x·3 + 3² = (2x – 3)².
Q15. The factorization of 12x + 36 is:
Factoring out the GCF 12 from 12x + 36 gives 12(x + 3), which is the correct factorization.
Chapter 4: Factorization and Algebraic Manipulation Revision Guide
Complete the MCQs first, then review every incorrect answer against the textbook heading where that concept appears. For biology and other science subjects, pay attention to terminology, diagrams, sequence of processes, examples and differences between similar structures or functions.
This chapter page keeps the exact class, subject, chapter, question count, answer checking, explanations and follow-up chapters together, so students can revise from one focused URL instead of searching through the full book again.
Class 9 Mathematics MCQ Preparation: Factorization and Algebraic Manipulation
This page supports Matric Part 1 practice in Mathematics. At this stage, the main purpose is building the definitions, symbols, rules and study habits needed for later matric work. The questions available here should be used with the current textbook and the instructions issued by the learner's school or examination board.
What Mathematics MCQs can test
In Mathematics, objective questions commonly draw on definitions, formulas, identities, properties, signs, graphs, theorem statements and short calculations. A useful answer is based on the exact wording and concept, not simply on recognising a familiar option. For this subject, learners should identify the rule being tested, perform the essential working separately and check signs, restrictions and units before selecting an option.
Factorization and Algebraic Manipulation: what to focus on
Definitions, notation, properties, formulas, restrictions and the logical steps needed to reach a valid result.
Complete the smallest useful calculation on paper and test whether the answer satisfies the original condition.
Common mistakes for Class 9 learners
In this subject, frequent errors include sign mistakes, using a formula outside its conditions, confusing similar properties or selecting an answer from mental arithmetic without verification. Separate new terms that look similar and connect every formula, rule or definition with at least one textbook example. When the page marks an answer as incorrect, the next step should be to identify the mistaken idea and verify it, rather than memorising the displayed answer letter.
A practical revision routine
Read a small textbook section, answer a focused set of MCQs and correct the underlying idea before starting the next section. Before attempting the MCQs, review formulas, identities, definitions, graph behavior, theorem conditions and representative solved examples. Complete a manageable set without notes, check the result, and divide errors into missing knowledge, misunderstood concepts and careless reading. Revise the appropriate section before repeating the chapter.
How to review Factorization and Algebraic Manipulation after the quiz
List the questions you missed from Factorization and Algebraic Manipulation and write the textbook heading connected with each one. Explain the correct idea in your own words, then return later and answer a fresh set. This gives the chapter page a clear purpose: finding specific weaknesses in Mathematics rather than only collecting a score.
Accuracy and responsible use
Explanations are provided where they exist in the question bank, but educational databases can contain incomplete or mistaken material. Confirm disputed answers with an authoritative textbook or teacher. Ahmad Learning Hub provides a practice resource and does not claim that a question will appear in an examination or that every available item represents an official board question.