ICSE Class 10

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

  1. 1.Without actual division, what is the remainder when the polynomial $p(x) = 8x^2 - 2x - 15$ is divided by $(2x + 3)$?
    • A.-6
    • B.0
    • C.6
    • D.12
  2. 2.The polynomial $px^3 + 4x^2 - 3x + q$ is completely divisible by $x^2 - 1$. What are the values of $p$ and $q$?
    • A.$p = 3$, $q = -3$
    • B.$p = 3$, $q = -4$
    • C.$p = -3$, $q = 4$
    • D.$p = 4$, $q = -3$
  3. 3.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.
  4. 4.Given that $(x + 2)$ and $(x + 3)$ are factors of the polynomial $x^3 + ax + b$, use the factor theorem to determine the completely factorized form of the polynomial.
    • A.$(x + 2)(x + 3)(x - 5)$
    • B.$(x + 2)(x + 3)(x + 5)$
    • C.$(x - 2)(x - 3)(x + 5)$
    • D.$(x + 2)(x - 3)(x - 5)$
  5. 5.For what value of $a$ is the polynomial $(2x^3 + ax^2 + 11x + a + 3)$ exactly divisible by $(2x - 1)$?
    • A.$a = 7$
    • B.$a = -7$
    • C.$a = 14$
    • D.$a = -14$

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