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.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.$a = 19$, $b = -30$
2. 2.If $x - 1$ and $x + 2$ both are factors of the polynomial $x^3 + (3m + 1)x^2 + nx - 18$, what are the values of $m$ and $n$?
   • A.$m = 1$, $n = -7$
   • B.$m = -1$, $n = 19$
   • C.$m = 2$, $n = 10$
   • D.$m = 0$, $n = 16$
3. 3.In the diagram below, the polynomial division process is illustrated for the expression $2x^{3} + 5x^{2} - 11x - 14$ by $2x + 7$. Identify the labelled part that represents the quotient obtained after division.
   • A.$x^2 - x - 2$
   • B.$2x^2 - x - 2$
   • C.$x^2 + x - 2$
   • D.$2x^2 + x + 2$
4. 4.If $(x + 2)$ and $(x + 3)$ are the factors of the polynomial $f(x) = x^3 + ax + b$, then the value of $a$ is
   • A.-19
   • B.-30
   • C.30
   • D.19
5. 5.Consider the assertion and reason below: 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 $p(x)$ if and only if $p(a) \geq 1$. Which is correct?
   • A.Assertion is true but reason is false
   • B.Assertion is false but reason is true
   • C.Both assertion and reason are true
   • D.Both assertion and reason are false