maths question - will give rep..when i can

Watch
This discussion is closed.
ShOcKzZ
Badges: 7
Rep:
?
#1
Report Thread starter 16 years ago
#1
p(x) = (x+2)^5

Find the remainder when p(x) is divided by (x+3)

how do i do this w/o finding the expansion of (x+2)^5.

thanks.
0
GH
Badges: 13
Rep:
?
#2
Report 16 years ago
#2
(Original post by ShOcKzZ)
p(x) = (x+2)^5

Find the remainder when p(x) is divided by (x+3)

how do i do this w/o finding the expansion of (x+2)^5.

thanks.
Let p(-3), and then you have (-3+2)^5, Remainder = -1
0
It'sPhil...
Badges: 2
Rep:
?
#3
Report 16 years ago
#3
Are you familiar with

p(x)/(x-a) = q(x) + R/(x-a)

Ie when you divide a polynomial by a linear factor x-a you get a polynomial plus some remainder over x-a.

This => p(x) = q(x)(x-a) + R
If we take x=a .......p(a) = 0 + R

So the remainder of p divided by x-a is equal to p(a).

This should be enough to answer the question
0
ShOcKzZ
Badges: 7
Rep:
?
#4
Report Thread starter 16 years ago
#4
(Original post by 2776)
Let p(-3), and then you have (-3+2)^5, Remainder = -1
thats what i thought. but, if you expand (x+2)^5, you get:

p(x) = x^5 + 10x^4 + 40x^3 + 80X^2 + 80x + 25
so:

p(-3) = -8
0
ShOcKzZ
Badges: 7
Rep:
?
#5
Report Thread starter 16 years ago
#5
(Original post by It'sPhil...)
Are you familiar with

p(x)/(x-a) = q(x) + R/(x-a)

Ie when you divide a polynomial by a linear factor x-a you get a polynomial plus some remainder over x-a.

This => p(x) = q(x)(x-a) + R
If we take x=a .......p(a) = 0 + R

So the remainder of p divided by x-a is equal to p(a).

This should be enough to answer the question
no, i didn't know that, lemme try it..
0
GH
Badges: 13
Rep:
?
#6
Report 16 years ago
#6
(Original post by It'sPhil...)
So the remainder of p divided by x-a is equal to p(a).

This should be enough to answer the question
Since (x-a) = [x+(-a)]

Therefore, [x+(-3)], and so remainder = a, therefore (-3) is correct.
0
It'sPhil...
Badges: 2
Rep:
?
#7
Report 16 years ago
#7
(Original post by ShOcKzZ)
thats what i thought. but, if you expand (x+2)^5, you get:

p(x) = x^5 + 10x^4 + 40x^3 + 80X^2 + 80x + 25
so:

p(-3) = -8
2^5 usually equals 32 not 25
0
ShOcKzZ
Badges: 7
Rep:
?
#8
Report Thread starter 16 years ago
#8
(Original post by It'sPhil...)
2^5 usually equals 32 not 25
oh ****

lol..so the -1 was correct..
0
X
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Are you travelling in the Uni student travel window (3-9 Dec) to go home for Christmas?

Yes (103)
28.69%
No - I have already returned home (46)
12.81%
No - I plan on travelling outside these dates (69)
19.22%
No - I'm staying at my term time address over Christmas (37)
10.31%
No - I live at home during term anyway (104)
28.97%

Watched Threads

View All