Polynomials ബഹുപദങ്ങൾ
Stretch every side of a rectangle by x cm: its perimeter becomes 4x + 10 and its area x² + 5x + 6. Stretch a block, and its volume becomes x³ + 6x² + 11x + 6. Rules like these, built only from powers of x, fixed numbers, multiplication and addition, are called polynomials. This chapter shows how measurements turn into polynomials, what the notation p(x) means, which expressions are polynomials and which are not, and what the degree and the coefficients of a polynomial are. This interactive, animated self-study guide has the basics from earlier classes, every idea of the chapter with real-life examples, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the animations
Rectangles stretch, blocks grow and cards fold into boxes, one step at a time. Press Next ▶ or ▶▶ Auto play.
🖐️ Play with x
Move the sliders to change x. The figure, the table of values and the polynomial all update together.
✍️ Try before you see
Every question has a Show a hint button and a hidden final answer. Work it out in your notebook first.
📖 Textbook links
Purple മലയാളം words are the exact terms used in your textbook (pages 177–184).
Learning path
Follow the pages in order. If you are comfortable with algebra, powers and multiplying brackets, you can skim pages 1–4, but still try their quizzes.
The chapter in one picture
The rectangle starts as 3 cm × 2 cm (blue). Every side is increased by x cm. The perimeter grows by four lots of x: p(x) = 4x + 10. The area splits into four pieces: 6 + 3x + 2x + x² = x² + 5x + 6.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| ബഹുപദം | Polynomial | An expression in which powers of x are multiplied by fixed numbers and added, e.g. x² + 5x + 6 |
| കൃത്യങ്കം | Degree | The biggest power of x in the polynomial: x³ + 6x² + 11x + 6 has degree 3 |
| ഗുണകങ്ങൾ | Coefficients | The fixed numbers multiplying the powers: a, b, c in ax² + bx + c |
| ഒന്നാംകൃതി ബഹുപദം | First degree polynomial | ax + b, e.g. 4x + 10 |
| രണ്ടാംകൃതി ബഹുപദം | Second degree polynomial | ax² + bx + c, e.g. x² + 5x + 6 |
| മൂന്നാംകൃതി ബഹുപദം | Third degree polynomial | ax³ + bx² + cx + d |
| കൃതി | Power | x² = x × x, x³ = x × x × x |
| ബീജഗണിതം | Algebra | Calculating with letters that stand for numbers |
| ചുറ്റളവ് · പരപ്പളവ് · വ്യാപ്തം | Perimeter · Area · Volume | The measures that become polynomials in this chapter |
| ചതുരക്കട്ട | Rectangular block (cuboid) | A box shape with length, breadth and height |
| വർഗമൂലം | Square root | √x. Taking the square root of x gives an expression that is not a polynomial |
| വ്യുൽക്രമം | Reciprocal | 1/x. Taking the reciprocal of x also gives an expression that is not a polynomial |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.