Question

Question 1 -

Classify the following as linear, quadratic and cubic polynomials:

[ i ] x² + x
[ ii ] x - x³
[ iii ] x + y² + 4
[ iv ] 1 + x
[ v ] 3 t
[ vi ] r²
[ vii ] 7x³

Question 2 -

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

Question 3 -

Write the coefficients of x²

in each of the following:

[ i ] 2 + x² + x
[ ii ] 2 - x² + x³
$\sf[ iii ] \frac{\pi}{2} x {}^{2} +x$
[ iv ] √2x - 1​

Answer 1

Question 1 -

Classify the following as linear, quadratic and cubic polynomials:

[ i ] x² + x

[ ii ] x - x³

[ iii ] x + y² + 4

[ iv ] 1 + x

[ v ] 3 t

[ vi ] r²

[ vii ] 7x³

Answer:-

Linear polynomial :-

• x + 1

• 3t

Quadratic polynomial :-

• x² + x

• x + y² + 4

• r²

Cubic polynomial :-

• x - x³

• 7x³

More Information:-

• Linear polynomial is a polynomial with degree 1.

• Quadratic polynomial is a polynomial with degree 2.

• Cubic polynomial is a polynomial with degree 3.

Question 2 -

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

Answer:-

• Binomial of degree 35 = 27x³⁵ + 97

• Monomial of degree 100 = x¹⁰⁰

More Information:-

• Binomial is a polynomial which contains 2 terms.

• Monomial is a polynomial with only 1 term.

• The terms in a polynomial are divided by these arithmetic operations :- +, -, *, /.

Question 3 -

Write the coefficients of x² in each of the following:

[ i ] 2 + x² + x

[ ii ] 2 - x² + x³

$\sf[ iii ] \frac{\pi}{2} x {}^{2} +x$

[ iv ] √2x - 1

Answer:-

Coefficients of x²:-

• [ i ] + 1

• [ ii ] - 1

• [ iii ] $\sf \dfrac{\pi}{2}$

• [ iv ] 0

Answer 2

Required Answer

1.

a) Quadratic

b) Cubic

c) Quadratic

d) Linear

e)  Linear

f) Quadratic

g) cubic

2.

a)$\bf x^{35}+ 11$

b)  y¹⁰⁰ + 5

3.

a) 1

b) -1

c)$\dfrac{\pi}{2}$

d) 0