Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Worksheet: Remainder and Factor Theorem
Worksheet: Remainder and Factor Theorem | Mathematics Class 10 ICSE PDF Download
A. Very Short Questions
Q1. Find the remainder when f(x) = x² + 3x – 5 is divided by x – 2.
Q2. If f(x) = 2x³ – 7x + 4, find the remainder when divided by x + 1.
Q3. Find the value of k if x – 3 is a factor of f(x) = x² + kx – 21.
Q4. Check whether x – 2 is a factor of f(x) = x³ – 3x² – 4x + 12.
Q5. Find the remainder when f(x) = 5x³ – 2x² + 7 is divided by x – 1.
B. Short Answer Questions
Q6. If f(x) = x³ + 2x² – kx – 10 and f(2) = 0, find the value of k.
Q7. If f(x) = ax³ – 2x² + 3 and f(1) = 5, find a.
Q8. Check if x + 2 is a factor of f(x) = 2x³ + 5x² – 4x – 20.
Q9. Find the remainder when f(x) = 3x³ – x² + 2 is divided by 3x – 1.
Q10. Find the value of m if (x – 1) is a factor of f(x) = x³ + mx² – 4x – 4.
C. Long Answer Questions
Q11. Show that x − 3 is a factor of f(x) = 2x³ − 3x² − 11x + 6 and factorise completely.
Q12. If x – 4 is a factor of f(x) = x³ – px² + qx – 24 and f(2) = 0, find p and q.
Q13. Factorise completely: f(x) = 2x³ + x² – 13x + 6.
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