## Chapter 2 Polynomials Exercise 2.1

Question 1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

i) 4x² - 3x + 7

ii) y² + √2

iii) 3√t + t√2

iv) y + 2/y

v) x¹⁰ + y³ + t⁵⁰

Answer:

i) and ii) are polynomials in one variable.

v) is a polynomial in three variable.

iii) and iv) are not polynomials as in each of these exponent of the variable is not a whole number.

Question 2: Write the coefficients of x² in each of the following:

i) 2 + x² + x

ii) 2 - x² + x³

iii) π/2 x² + x

iv) √2 x - 1

Answer:

i) 1

ii) -1

iii) π/2

iv) 0

Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:

Binomial of degree 35: x³⁵ - 5

Monomial of degree 100: y¹⁰⁰

Question 4: Write the degree of each of the following polynomials:

i) 5x³ + 4x² + 7x

ii) 4 - y²

iii) 5t - √7

iv) 3

Answer:

i) 3

ii) 2

iii) 1

iv) 0

Question 5: Classify the following as linear, quadratic and cubic polynomials:

i) x² + x

ii) x - x³

iii) y + y² + 4

iv) 1 + x

v) 3t

vi) r²

vii) 7x³

Answer:

i) Quadratic

ii) Cubic

iii) Quadratic

iv) Linear

v) Linear

vi) Quadratic

vii) Cubic

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