Example 1 · level 1
Find the remainder when x² + 5x − 5 is divided by (x + 1).
Show solution
- x + 1 = 0 gives x = −1.
- p(−1) = (−1)² + 5 × (−1) − 5
- = −9. So the remainder is −9.
Answer: -9
CLASS 9 MATHS · POLYNOMIALS
Remainder theorem
When p(x) is divided by (x − a), the remainder is p(a). For (x + a), use p(−a).
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Worked examples
Example 2 · level 2
Find the remainder when x³ − 2x² + 4x − 4 is divided by (x − 2).
Show solution
- x − 2 = 0 gives x = 2.
- p(2) = 2³ − 2 × 2² + 4 × 2 − 4
- = 4. So the remainder is 4.
Answer: 4
Example 3 · level 3
Find the remainder when 3x³ + 2x² − x − 7 is divided by (x + 4).
Show solution
- x + 4 = 0 gives x = −4.
- p(−4) = 3 × (−4)³ + 2 × (−4)² − (−4) − 7
- = −163. So the remainder is −163.
Answer: -163