a. Answer Order the function from least degree to greatest degree is 4 x + 10 x − 4 x 2 − 4 x 3 − 3 x 4 Explanation Given information : f ( x ) = 2 x 3 − 4 x 2 + 8 x − 1 g ( x ) = 2 x − 3 x 4 − 6 x 3 + 5 h ( x ) = − 7 + x 2 + x Calculation : ( f + g ) ( x ) = f ( x ) + g ( x ) = 2 x 3 − 4 x 2 + 8 x − 1 + 2 x − 3 x 4 − 6 x 3 + 5 = − 3 x 4 − 4 x 3 − 4 x 2 + 10 x + 4 x = 4 + 10 x − 4 x 2 − 4 x 3 − 3 x 4 Hence, order the function from least degree to greatest degree is 4 + 10 x − 4 x 2 − 4 x 3 − 3 x 4 . b. To determine To write : Order the function from least degree to greatest degree Answer Order the function from least degree to greatest degree is − 35 − 9 x + 7 x 2 + 44 x 3 + 15 x 4 − 9 x 5 − 3 6 Explanation Given information : f ( x ) = 2 x 3 − 4 x 2 + 8 x − 1 g ( x ) = 2 x − 3 x 4 − 6 x 3 + 5 h ( x ) = − 7 + x 2 + x Calculation : ( h g ) ( x ) = h ( x ) ⋅ g ( x ) = ( − 7 + x 2 + x ) ( 2 x − 3 x 4 − 6 x 3 + 5 ) = − 14 x + 2 x 3 + 2 x 2 + 21 x 4 − 3 x 6 − 3 x 5 + 42 x 3 − 6 x 5 − 6 x 4 − 35 + 5 x 2 + 5 x = − 35 − 9 x + 7 x 2 + 44 x 3 + 15 x 4 − 9 x 5 − 3 6 Hence, order the function from least degree to greatest degree is − 35 − 9 x + 7 x 2 + 44 x 3 + 15 x 4 − 9 x 5 − 3 6 . c. To determine To write : Order the function from least degree to greatest degree Answer Order the function from least degree to greatest degree is − 6 − 7 x + 5 x 2 − 2 x 3 Explanation Given information : f ( x ) = 2 x 3 − 4 x 2 + 8 x − 1 g ( x ) = 2 x − 3 x 4 − 6 x 3 + 5 h ( x ) = − 7 + x 2 + x Calculation : ( h − f ) ( x ) = h ( x ) − f ( x ) = ( − 7 + x 2 + x ) − ( 2 x 3 − 4 x 3 + 8 x − 1 ) = − 7 + x 2 + x − 2 x 3 + 4 x 3 − 8 x + 1 = − 6 − 7 x + 5 x 2 − 2 x 3 Hence, order the function from least degree to greatest degree is − 6 − 7 x + 5 x 2 − 2 x 3 . d. To determine To write : Order the function from least degree to greatest degree Answer Order the function from least degree to greatest degree is 35 x 2 − 10 x 3 − 2 x 4 + 2 x 5 Explanation Given information : f ( x ) = 2 x 3 − 4 x 2 + 8 x − 1 g ( x ) = 2 x − 3 x 4 − 6 x 3 + 5 h ( x ) = − 7 + x 2 + x Calculation : ( f h ) ( x ) = f ( x ) ⋅ h ( x ) = ( 2 x 3 − 4 x 2 + 8 x − 1 ) ( − 7 + x 2 − x ) = − 14 x 3 + 28 x 2 − 56 x + 7 + 2 x 5 − 4 x 4 + 8 x 3 − x 2 + 2 x 4 − 4 x 3 + 8 x 2 − x = 35 x 2 − 10 x 3 − 2 x 4 + 2 x 5 Hence, order the function from least degree to greatest degree is 35 x 2 − 10 x 3 − 2 x 4 + 2 x 5 .

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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Question

Chapter 6, Problem 6CA

To determine

To write : Order the function from least degree to greatest degree

Expert Solution

Answer to Problem 6CA

Order the function from least degree to greatest degree is 4x+10x−4x2−4x3−3x4

Explanation of Solution

Given information :

f(x)=2x3−4x2+8x−1g(x)=2x−3x4−6x3+5h(x)=−7+x2+x

Calculation :

(f+g)(x)=f(x)+g(x)=2x3−4x2+8x−1+2x−3x4−6x3+5=−3x4−4x3−4x2+10x+4x=4+10x−4x2−4x3−3x4

Hence, order the function from least degree to greatest degree is 4+10x−4x2−4x3−3x4 .

To determine

To write : Order the function from least degree to greatest degree

Expert Solution

Answer to Problem 6CA

Order the function from least degree to greatest degree is −35−9x+7x2+44x3+15x4−9x5−36

Explanation of Solution

Given information :

f(x)=2x3−4x2+8x−1g(x)=2x−3x4−6x3+5h(x)=−7+x2+x

Calculation :

(hg)(x)=h(x)⋅g(x)=(−7+x2+x)(2x−3x4−6x3+5)=−14x+2x3+2x2+21x4−3x6−3x5+42x3−6x5−6x4−35+5x2+5x=−35−9x+7x2+44x3+15x4−9x5−36

Hence, order the function from least degree to greatest degree is −35−9x+7x2+44x3+15x4−9x5−36 .

To determine

To write : Order the function from least degree to greatest degree

Expert Solution

Answer to Problem 6CA

Order the function from least degree to greatest degree is −6−7x+5x2−2x3

Explanation of Solution

Given information :

f(x)=2x3−4x2+8x−1g(x)=2x−3x4−6x3+5h(x)=−7+x2+x

Calculation :

(h−f)(x)=h(x)−f(x)=(−7+x2+x)−(2x3−4x3+8x−1)=−7+x2+x−2x3+4x3−8x+1=−6−7x+5x2−2x3

Hence, order the function from least degree to greatest degree is −6−7x+5x2−2x3 .

To determine

To write : Order the function from least degree to greatest degree

Expert Solution

Answer to Problem 6CA

Order the function from least degree to greatest degree is 35x2−10x3−2x4+2x5

Explanation of Solution

Given information :

f(x)=2x3−4x2+8x−1g(x)=2x−3x4−6x3+5h(x)=−7+x2+x

Calculation :

(fh)(x)=f(x)⋅h(x)=(2x3−4x2+8x−1)(−7+x2−x)=−14x3+28x2−56x+7+2x5−4x4+8x3−x2+2x4−4x3+8x2−x=35x2−10x3−2x4+2x5

Hence, order the function from least degree to greatest degree is 35x2−10x3−2x4+2x5 .

Chapter 6, Problem 5CA

Chapter 6, Problem 7CA

Chapter 6 Solutions

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

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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