Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Chapter 4.5, Problem 66E
To determine

Whether the given function is polynomial function or not. Also write the polynomial function is standard form and write the type, degree, and leading coefficient of the polynomial function.

Expert Solution & Answer
Check Mark

Answer to Problem 66E

The given function is polynomial function.

Standard form is h(x)=4x33x2+2x9 .

Degree of the polynomial function is 3.

Leading coefficient will be 2 .

Given function is a cubic polynomial.

Explanation of Solution

Given information:

A function is given as

  h(x)=3x2+2x9+4x3

Concept used:

A polynomial function is of the form

  f(x)=anxn+an1xn1+...+a1x+a0

Terms of a polynomial function should be arranged in descending order according to its degree to express it in a standard form and degree of each term should be a positive integer or whole number. The coefficients should be real numbers.

Leading coefficient of a polynomial function is the coefficient of the leading term.

Degree of the polynomial is the degree of leading term or the height degree in the polynomial function.

For the polynomial f(x)=anxn+an1xn1+...+a1x+a0 the leading coefficient is an and the degree is n .

Calculation:

Consider the given function.

  h(x)=3x2+2x9+4x3

Now, degree of each term is a whole number and all coefficients are real.

So, the function is polynomial function.

The polynomial function can be written in its standard form by arranging the terms in descending order according to its degree.

Now, write the function in its standard form as shown:

  h(x)=4x33x2+2x9

Now, degree of the polynomial function is 3.

Leading term is 4x3 .

So, leading coefficient will be 2 .

As, degree of the polynomial function is 3, so it is a cubic polynomial.

Chapter 4 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - 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