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.

Sample questions

1. 1.Use the Remainder Theorem to factorise the expression: $2x^3 + x^2 - 13x + 6$. Which of the following is the correct factorisation?
   • A.$(x - 2)(2x - 1)(x + 3)$
   • B.$(x + 2)(2x - 1)(x - 3)$
   • C.$(x - 2)(2x + 1)(x + 3)$
   • D.$(2x - 2)(x - 1)(x + 3)$
2. 2.Assertion: $(x + 2)$ and $(x - 1)$ are factors of the polynomial $x^4 + x^3 + 2x^2 + 4x - 8$. Reason: For a polynomial $p(x)$ of degree $\geq 1$, $x - a$ is a factor of the polynomial $p(x)$ if and only if $p(a) \geq 1$.
   • A.Both assertion and reason are true and reason is the correct explanation of assertion.
   • B.Both assertion and reason are true but reason is not the correct explanation of assertion.
   • C.Assertion is true but reason is false.
   • D.Assertion is false but reason is true.
3. 3.Find the values of constants $a$ and $b$ when $x - 2$ and $x + 3$ both are the factors of expression $x^3 + ax^2 + bx - 12$.
4. 4.Using the factor theorem, which of the following is the correct factorization of the polynomial $6x^3 - 7x^2 - 11x + 12$?
   • A.$(x - 1)(2x + 3)(3x - 4)$
   • B.$(x - 1)(2x - 3)(3x + 4)$
   • C.$(x + 1)(2x - 3)(3x + 4)$
   • D.$(x - 1)(6x^2 - x - 12)$
5. 5.If $(x + 2)$ and $(x + 3)$ are factors of $x^3 + ax + b$, determine the values of $a$ and $b$ respectively.
   • A.$a = -19$, $b = -30$
   • B.$a = 19$, $b = 30$
   • C.$a = -19$, $b = 30$
   • D.$a = 19$, $b = -30$