Exercise 2.1

1. Find the degree of each of the polynomials given below:

i. x5 - x4 + 3

Solution:

The biggest power of x is .

So the degree is .

ii. x2 + x - 5

Solution:

The biggest power of x is .

So the degree is .

iii. 5

Solution:

This is just a .

The degree is .

iv. 3x6 + 6y3 - 7

Solution:

The biggest power is .

So the degree is .

v. 4 - y2

Solution:

The biggest power of y is .

So the degree is .

vi. 5t - 3

Solution:

The biggest power of t is .

So the degree is .

2. Which of the following expressions are polynomials in one variable and which are not? Give reasons for your answer.

i. 3x2 - 2x + 5

Solution:

Is it a polynomial: YesNo

It only has x's.

ii. x2 + 2

Solution:

Is it a polynomial: YesNo

It only has x's.

iii. p2 - 3p + q

Solution:

Is it a polynomial: YesNo

It has p's and q's.

iv. y + 1y2 (y ≠ 0)

Solution:

Is it a polynomial: NoYes

The y is on the bottom of the fraction.

v. 5x + xsqrt5

Solution:

Is it a polynomial: NoYes

There's a square root of x.

vi. x100 + y100

Solution:

Is it a polynomial: NoYes

It has x's and y's.

3. Write the coefficient of x3 in each of the following:

i. x3 + x + 1

Solution:

ii. 2 - x3 + x2

Solution:

iii. 32x + 5

Solution:

iv. 2x3 + 5

v. (3/2)x + πx3

π1

vi. 23 - x3

Solution:

vii. 2x2 + 5

Solution:

viii. 4

Solution:

4. Classify the following as linear, quadratic, and cubic polynomials:

i. 5x2 + x - 7

Solution:

QuadraticCubic

ii. x - x3

Solution:

CubicQuadratic

iii. x2 + x + 4

Solution:

QuadraticCubic

iv. x - 1

Solution:

LinearQuadratic

v. 3p

Solution:

LinearCubic

vi. πr2

Solution:

QuadraticLinear

5. Write whether the following statements are True or False. Justify your answer.

i. A binomial has two terms.

Solution:

TrueFalse

ii. Every polynomial is a binomial.

Solution:

FalseTrue

iii. A binomial may have degree 3.

Solution:

TrueFalse

iv. Degree of zero polynomial is zero.

Solution:

FalseTrue

v. The degree of x2 + 2xy + y2 is 2.

Solution:

TrueFalse

vi. πr2 is a monomial.

Solution:

TrueFalse

6. Give one example each of a monomial and trinomial of degree 10.

Solution:

Monomial (one term): x10x10+3 (anything with only term and the highest power is )

Trinomial (three terms): x10+x5+1x10+x11+1 (with terms where the highest power is )