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.Use the factor theorem to determine which of the following statements correctly shows that $(x + 2)$ and $(2x - 3)$ are factors of the polynomial $(2x^2 + x - 6)$?
- A.$p(-2) = 0$ and $p\left(\frac{3}{2}\right) = 0$, confirming both are factors.
- B.$p(2) = 0$ and $p\left(-\frac{3}{2}\right) = 0$, confirming both are factors.
- C.$p(-2) = 0$ only, so only $(x + 2)$ is a factor.
- D.$p\left(\frac{3}{2}\right) = 2$ and $p(-2) = -4$, so neither is a factor.
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2.(i) Using the Factor theorem, it is shown that $(x - 3)$ is a factor of $x^3 - 7x^2 + 15x - 9$. Which of the following represents the complete factorization of the given polynomial?
- A.$(x - 1)(x - 3)^2$
- B.$(x - 3)(x^2 - 4x + 3)$
- C.$(x - 1)^2(x - 3)$
- D.$(x - 3)(x^2 - 6x + 9)$
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3.If $x - 2$ is a factor of the expression $x^3 + ax^2 + bx + 6$. When the expression is divided by $(x - 3)$, it leaves a remainder 3. Then the values of $a$ and $b$ respectively are:
- A.$-4, 1$
- B.$1, 4$
- C.$-1, 4$
- D.$4, -1$
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4.If $(x - 2)$ and $(x + 3)$ are factors of the quadratic polynomial $x^2 + (a + 1)x + b$, then find the value of $a$ and $b$.
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5.What is the remainder when $2x^{3} - 3x^{2} + 7x - 8$ is divided by $x - 1$?
- A.$-1$
- B.$0$
- C.$-2$
- D.$2$
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