Chapter 5: Q. 8 (page 497)

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

Short Answer

Expert verified

The type and degree of the polynomials is

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

Step by step solution

Step 1. Given information

The given polynomial expressions are

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

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

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

Step 3. Determine the degree

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the type

Step 3. Determine the degree

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In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial(a)15xy(b)15(c)6x2−3xy+4x−2y+y2(d)10p−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

Pure Maths

Decision Maths

Logic and Functions

Applied Mathematics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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