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.Using the factor theorem, if $(x - 3)$ is a factor of $x^3 - 7x^2 + 15x - 9$, which of the following is its complete factorisation?
- A.$(x - 3)^2(x - 1)$
- B.$(x - 3)(x - 1)^2$
- C.$(x + 3)^2(x - 1)$
- D.$(x - 3)(x + 1)(x - 3)$
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2.If $x - 2$ is a factor of $x^2 + ax + b$ and $a + b = 1$, what are the values of $a$ and $b$?
- A.$a = -3$, $b = 4$
- B.$a = -5$, $b = 6$
- C.$a = 3$, $b = -2$
- D.$a = -1$, $b = 2$
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3.Given that $x - 2$ and $x + 1$ are factors of $f(x) = x^3 + 3x^2 + ax + b$, calculate the values of $a$ and $b$. Which of the following correctly represents the values of $a$ and $b$ and the complete factorization of $f(x)$?
- A.$a = -4$, $b = -4$; Factors: $(x - 2)(x + 1)(x + 2)$
- B.$a = 4$, $b = -4$; Factors: $(x - 2)(x + 1)(x - 2)$
- C.$a = -4$, $b = 4$; Factors: $(x - 2)(x + 1)(x + 4)$
- D.$a = 4$, $b = 4$; Factors: $(x - 2)(x + 1)(x - 1)$
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4.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. What is the value of $p$?
- A.$p = 1$
- B.$p = -1$
- C.$p = 2$
- D.$p = -2$
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5.Find the remainders when the polynomial $3x^{3} - 4x^{2} + 7x - 5$ is divided by $x - 3$ and $x + 3$ respectively.
- A.61 and -143
- B.52 and -134
- C.67 and -150
- D.70 and -140
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