The perimeter of a square of side x is 4x, which is a linear polynomial in the variable x.
Answer: Perimeter = x + x + x + x = 4x. The highest power of x is 1, so 4x is a linear polynomial.
Step-by-step solution
Idea: A linear polynomial is a polynomial of degree 1: the variable appears only to the power 1 (and there may be a constant).
- A square has 4 equal sides, each x. Perimeter = x + x + x + x = 4x.1 mark
- In 4x = 4x1, the only power of x is 1. So its degree is 1 and 4x is a linear polynomial in x.1 mark
- For example, side 3 cm gives perimeter 4 × 3 = 12 cm, and side 5 cm gives 20 cm.
The perimeter of a square of side x is 4x, a polynomial of degree 1, that is, a linear polynomial.
Answer to write in the exam
Perimeter of square = x + x + x + x = 4x
Highest power of x in 4x = 1
∴ 4x is a linear polynomial in x
Common mistakes that cost marks
- Writing the perimeter as x4 (multiplying the sides instead of adding them).
- Confusing perimeter with area. The area x2 has degree 2, so it is not linear.
- Thinking 4x is not a polynomial because it has only one term. A single term like 4x is still a polynomial.
How this can come in the exam
MCQ (1 mark)
Which of these is a linear polynomial?
- a2
- 6a
- a3 + 1
- 7
Show answer
(B) 6a
6a has degree 1. a2 has degree 2, a3 + 1 degree 3, and 7 degree 0.
Short answer (2 marks)
The side of an equilateral triangle is s cm. Write its perimeter as a polynomial and state its degree.
Show answer
Perimeter = s + s + s = 3s cm (1 mark). Highest power of s is 1, so the degree is 1: a linear polynomial (1 mark).Try one yourself
A regular hexagon has side k m. Write its perimeter. Is it a linear polynomial?
Show answer
6k m. Yes, its degree is 1.
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