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.The factor common to the two polynomials $x^2 - 4$ and $x^3 - x^2 - 4x + 4$ is:
- a.$(x + 1)$
- b.$(x - 1)$
- c.$(x - 2)$
- d.$(x - 4)$
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2.Factorise the expression $f(x) = 2x^3 - 7x^2 - 3x + 18$. Which of the following represents the correct factorisation and the possible values of $x$ for which $f(x) = 0$?
- A.$(x - 2)(2x + 3)(x - 3)$; $x = 2$, $x = - rac{3}{2}$, $x = 3$
- B.$(x + 2)(2x - 3)(x - 3)$; $x = -2$, $x = rac{3}{2}$, $x = 3$
- C.$(x - 2)(2x - 3)(x + 3)$; $x = 2$, $x = rac{3}{2}$, $x = -3$
- D.$(2x - 2)(x + 3)(x - 3)$; $x = 1$, $x = -3$, $x = 3$
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3.Show that $(3x + 2)$ is a factor of $(6x^3 + 13x^2 - 4)$. Which of the following is the complete factorization of $(6x^3 + 13x^2 - 4)$?
- A.$(3x + 2)(x + 2)(2x - 1)$
- B.$(3x + 2)(2x^2 + 3x - 2)$
- C.$(3x - 2)(2x + 1)(x + 2)$
- D.$(6x^2 + x - 2)(x + 2)$
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4.Find the value of $a$, if $(x - a)$ is a factor of $x^3 - ax^2 + x + 2$.
- A.-2
- B.-1
- C.1
- D.2
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5.Given that $x - 3$ is a factor of the polynomial $2x^{3} - x^{2} - 13x - 6$, which of the following represents its complete factorisation?
- A.$(x - 3)(2x + 1)(x + 2)$
- B.$(x + 3)(2x - 1)(x - 2)$
- C.$(x - 3)(2x - 1)(x + 2)$
- D.$(x + 3)(2x + 1)(x - 2)$
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