Example 1 · level 1
Find k if (x + 2) is a factor of x² + kx + 8.
Show solution
- p(−2) = 0.
- Substituting: 12 − 2k = 0.
- −2k = −12 → k = 6.
Answer: 6
CLASS 9 MATHS · POLYNOMIALS
Factor theorem: find the missing coefficient
(x − a) is a factor of p(x) exactly when p(a) = 0. Put x = a, set the result to 0 and solve.
Loading practice…
Worked examples
Example 2 · level 2
Find k if (x − 3) is a factor of x³ + 3x² + kx − 72.
Show solution
- p(3) = 0.
- Substituting: −18 + 3k = 0.
- 3k = 18 → k = 6.
Answer: 6
Example 3 · level 3
Find k if (x + 3) is a factor of x³ + kx² − 5x − 60.
Show solution
- p(−3) = 0.
- Substituting: −72 + 9k = 0.
- 9k = 72 → k = 8.
Answer: 8