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.When divided by $x - 3$ the polynomials $x^3 - px^2 + x + 6$ and $2x^3 - x^2 - (p + 3)x - 6$ leave the same remainder. Find the value of $p$.
- A.1
- B.3/2
- C.-1
- D.2
-
2.When $f(x) = x^3 + ax^2 - bx - 8$ is divided by $x - 2$, the remainder is zero and when divided by $x + 1$, the remainder is $-30$. What are the values of $a$ and $b$?
- A.a = -7, b = -14
- B.a = 7, b = 14
- C.a = -5, b = -16
- D.a = -9, b = -12
-
3.Find the value of $a$ if $x - a$ is a factor of the polynomial $3x^3 + x^2 - ax - 81$.
- A.$a = 3$
- B.$a = -3$
- C.$a = 9$
- D.$a = -9$
-
4.If both $(x - 2)$ and $(2x - 1)$ are factors of $ax^2 + 5x + b$, which of the following must be true?
- A.$a + b = 0$
- B.$a - b = 0$
- C.$a = 2b$
- D.$a = -b$
-
5.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.$(2x - 2)(x + 3)(x - 3)$; $x = 1$, $x = -3$, $x = 3$
Ready? Take the full 20-question test free — instant marking, no sign-up needed.
▶ Start free mock test