POLYNOMIALS VOCABULARY

What is polynomial ?

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.

The algebraic terms which has the power as rational numbers or negative cannot be considered as polynomial.

Classifying Polynomials

• Classifying polynomials
• Identify monomial binomial and trinomial
• Classifying polynomial worksheet 

Problem 1 :

True or false :

2x is a monomial.

Solution :

Number of terms in 2x is 1, so it must be a monomial.

Problem 2 :

Constant term in x - 2

Solution :

Constant is a numerical value, then -2 is the constant.

Problem 3 :

True or false :

There can be a binomial of degree 5.

Solution :

Yes, binomial should consists of only two terms. One of the term may have the highest exponent of 5.

For example, 

2x⁵ + 3

Problem 4 :

The remainder when x² - 1 is divided by x - 1 _______

Solution :

Let p(x) = x² - 1

x - 1 = 0

x = 1

p(1) = 1² - 1

= 1 - 1

= 0

So, the remainder is 0.

Problem 5 :

A polynomial having three terms is called ______

Solution :

A polynomial which consist of three terms is known as trinomial.

Problem 6 :

The degree of x⁵ + 3x⁴ - 7x is _____

Solution :

The given polynomial is in standard form, the degree of the polynomial is the highest exponent. Then the degree of the polynomial is 5.

Problem 7 :

A real number k is called zero of a polynomial if _______

Solution :

The real number is k, when dividing the given polynomial by x - k if we get 0 as remainder then we will conclude k is a zero.

Problem 8 :

A quadratic polynomial can have one zero (true or false)

Solution :

The polynomial is known as quadratic when the highest exponent is 2.

• If those two zeroes are the same, we may decide there is only one zero. Then it is true.
• If those two zeroes are different, the given statement will become false.

Problem 9 :

Rewrite the following polynomial is descending order 

5x - 4 - 3x⁴ + 2x²

Solution :

The descending order is arranging the polynomial from greater exponent to the least exponent.

- 3x⁴ + 2x² + 5x - 4

Problem 10 :

What is the leading coefficient of the polynomial ?

a) 2x⁴ + 7x² - 18

b) -x³ + 2x² - 5x + 13

Solution :

The highest exponent of the polynomial is degree and its coefficient is the leading coefficient of the polynomial.

a) Degree = 4

Leading coefficient = 2

b) Degree = 3

Leading coefficient = -1

Problem 11 :

What is the degree of the polynomial

-8x - 3x⁵ + 10 + 6x⁴ 

Solution :

The highest exponent of the polynomial is 5. So, the degree of the polynomial is 5.

Problem 12 :

What is the degree of the polynomial

-8x - 3x⁵ + 10 + 6x⁴ 

Solution :

The highest exponent of the polynomial is 5. So, the degree of the polynomial is 5.

Problem 13 :

Match the term with its description

Solution :

1) _____ binomial

c.  A polynomial with two terms.

2) _____ standard form

d.  Written with terms in descending order, from largest degree to smallest degree.

3) ____ leading coefficient

g.  The number in front of the first term of a polynomial.

4) ____ monomial

a.  A polynomial with only one term.

5) _____ degree of a monomial

i.  The first term of a polynomial.

6) _______ degree of a polynomial

f.  The value of the sum of the exponent of the variables in a term

7) _____ constant

b.  The number that does not multiply any power of x.

8) ____ trinomial

h.  A polynomial with three terms.