Q. 8 In the following exercises, dete... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 8 (page 497)

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial
$\begin{array}{l} (a) 15 x y \\ (b) 15 \\ (c) 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} \\ (d) 10 p 鈭� 9 q \\ (e) m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 \end{array}$

Short Answer

Expert verified

The type and degree of the polynomials is

$\begin{matrix} Polynomial & Type & Degree \\ a) & 15 x y & Monomial & 2 \\ b) & 15 & Monomial & 0 \\ c) & 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} & Polynomial & 2 \\ d) & 10 p 鈭� 9 q & Binomial & 1 \\ e) & 鈭� m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 & Polynomial & 4 \end{matrix}$

Step by step solution

Step 1. Given information

The given polynomial expressions are

$\begin{array}{l} (a) 15 x y \\ (b) 15 \\ (c) 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} \\ (d) 10 p 鈭� 9 q \\ (e) m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 \end{array}$

We have to determine whether each polynomial is a monomial, binomial, trinomial, or other polynomials.

Also, we have to determine the degree of each polynomial.

Step 2. Determine the type

$\begin{matrix} Polynomial & Numberofterms & Type \\ a) & 15 x y & 1 & Monomial \\ b) & 15 & 1 & Monomial \\ c) & 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} & 5 & Polynomial \\ d) & 10 p 鈭� 9 q & 2 & Binomial \\ e) & 鈭� m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 & 5 & Polynomial \end{matrix}$

Step 3. Determine the degree

$\begin{matrix} Polynomial & Degreeofterms & Degree \\ a) & 15 x y & 2 & 2 \\ b) & 15 & 0 & 0 \\ c) & 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} & 2, 2, 1, 1, 2 & 2 \\ d) & 10 p 鈭� 9 q & 1, 1 & 1 \\ e) & 鈭� m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 & 4, 3, 2, 1, 0 & 4 \end{matrix}$

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91影视

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial
$\begin{array}{l} (a) 15 x y \\ (b) 15 \\ (c) 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} \\ (d) 10 p 鈭� 9 q \\ (e) m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the type

Step 3. Determine the degree

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91影视

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial(a)15xy(b)15(c)6x2鈭�3xy+4x鈭�2y+y2(d)10p鈭�9q(e)m4+4m3+6m2+4m+1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the type

Step 3. Determine the degree

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial
$\begin{array}{l} (a) 15 x y \\ (b) 15 \\ (c) 6 x^{2} 鈭� 3 x y + 4 x 鈭� 2 y + y^{2} \\ (d) 10 p 鈭� 9 q \\ (e) m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 \end{array}$