ICSE Class 10 Factorization of Polynomials — Mock Test (2027)
Free online mock test for Factorization of Polynomials (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Factorization of Polynomials chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Find $a$ if the two polynomials $ax^3 + 3x^2 - 9$ and $2x^3 + 4x + a$ leave the same remainder when divided by $x + 3$.
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2.If $(x - 2)$ is a factor of the expression $2x^3 + ax^2 + bx - 14$ and when the expression is divided by $(x - 3)$, it leaves a remainder 52, find the values of $a$ and $b$.
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3.Using the Remainder Theorem, which of the following is the complete factorisation of the polynomial $x^3 + 10x^2 - 37x + 26$?
- A.$(x - 1)(x + 2)(x + 13)$
- B.$(x - 1)(x - 2)(x + 13)$
- C.$(x + 1)(x - 2)(x - 13)$
- D.$(x - 1)(x + 2)(x - 13)$
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4.The polynomials $ax^3 + 3x^2 - 3$ and $2x^3 - 5x + a$, when divided by $x - 4$, leave the same remainder in each case. What is the value of $a$?
- A.1
- B.-1
- C.2
- D.0.5
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5.The polynomial, $f(x) = x^4 - 2x^3 + 3x^2 - ax + b$ when divided by $(x - 1)$ and $(x + 1)$ leaves the remainders 5 and 19 respectively. What are the values of $a$ and $b$, and what is the remainder when $f(x)$ is divided by $(x - 2)$?
- A.$a = 5$, $b = 8$, remainder = 10
- B.$a = 3$, $b = 6$, remainder = 8
- C.$a = 4$, $b = 7$, remainder = 12
- D.$a = 6$, $b = 9$, remainder = 6
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