My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 27th, 2016, 02:08 PM   #1
Newbie
 
Joined: Aug 2016
From: England

Posts: 3
Thanks: 0

Find the coefficient of x^4 in the expansion...

Evening guys, ok so i have a problem that has me stumped, i have been taking a look at it for quite some time whilst drinking my coffee and i am still not sure what theorem or method to use to solve it other than the fact that it obviously requires some form of expanding/simplifying algebra.

The question itself:

Find the coefficient of x^4 in the expansion of:

x(x^2 + 2x +3)(x^2 + 7x - 2)

Am not sure how i am meant to identify the coefficient of x^4.

Any help would be appreciated

PS: Am not sure if this is the right section for this post, please feel free to move it to the correct section if it is necessary
Furai is offline  
 
August 27th, 2016, 02:27 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,202
Thanks: 1157

Quote:
Originally Posted by Furai View Post
Evening guys, ok so i have a problem that has me stumped, i have been taking a look at it for quite some time whilst drinking my coffee and i am still not sure what theorem or method to use to solve it other than the fact that it obviously requires some form of expanding/simplifying algebra.

The question itself:

Find the coefficient of x^4 in the expansion of:

x(x^2 + 2x +3)(x^2 + 7x - 2)

Am not sure how i am meant to identify the coefficient of x^4.

Any help would be appreciated

PS: Am not sure if this is the right section for this post, please feel free to move it to the correct section if it is necessary
after you multiply all that out you will have a polynomial in x of the form

$c_0 + c_1 x + c_2 x^2 + c_3 x^3 + c_4 x^4 + c_5 x^5$

$c_4$ is the coefficient of $x^4$

You have two ways of going about it

a) just do the multiplication and combine terms of the same power of x to obtain the form above and then just read off $c_4$

b) try and be a bit more clever by determining ahead of time which multiplications will end up with $x^4$ and just combining those terms.

If I was dumping it into software I'd do (a). If I was doing it by hand I'd do (b)
romsek is offline  
August 27th, 2016, 02:31 PM   #3
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,781
Thanks: 1432

Quote:
Originally Posted by Furai View Post
Evening guys, ok so i have a problem that has me stumped, i have been taking a look at it for quite some time whilst drinking my coffee and i am still not sure what theorem or method to use to solve it other than the fact that it obviously requires some form of expanding/simplifying algebra.

The question itself:

Find the coefficient of x^4 in the expansion of:

x(x^2 + 2x +3)(x^2 + 7x - 2)

Am not sure how i am meant to identify the coefficient of x^4.

Any help would be appreciated

PS: Am not sure if this is the right section for this post, please feel free to move it to the correct section if it is necessary
note that expanding $(x^2 + 2x +3)(x^2 + 7x - 2)$ yields a cubic term of $7x^3 + 2x^3 = 9x^3$ ... multiplying by the $x$ out front makes that cubic term a quartic term of $9x^4$
skeeter is offline  
August 27th, 2016, 02:45 PM   #4
Newbie
 
Joined: Aug 2016
From: England

Posts: 3
Thanks: 0

Quote:
Originally Posted by skeeter View Post
note that expanding $(x^2 + 2x +3)(x^2 + 7x - 2)$ yields a cubic term of $7x^3 + 2x^3 = 9x^3$ ... multiplying by the $x$ out front makes that cubic term a quartic term of $9x^4$
So 9 would be the coefficient?
Furai is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
coefficient, expansion, find



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Coefficient find in expansion of a term Shen Algebra 1 January 17th, 2015 03:47 PM
Find coefficient of polynomial that matches limit PhizKid Calculus 5 October 3rd, 2012 12:12 PM
infinite binomial expansion to find e ershi Abstract Algebra 0 November 1st, 2011 09:44 AM
Find correlation coefficient? daivinhtran Algebra 4 May 14th, 2011 01:35 PM
how to find the coefficient of this polynomial davedave Algebra 1 November 10th, 2009 01:26 AM





Copyright © 2018 My Math Forum. All rights reserved.