Polynomial question (1 Viewer)

[YBK]

Hey, I have a question which I'd be grateful someone can help me with

A polynomial is given by P(x) = x^3 + ax^2 + bx + 6

Find the values of a and b if (x+3) is a factor and if 12 is the remainder when P(x) is divided by (x+1)

These kind of questions are really annoying me... especially that I can't even find a chapter about the remainder theorm and such in my cambridge book!

I was thinking of maybe using the division transformation... i end up with a - b = 7
Ummm.. i'm stuck!


thanks everyone!

 

[richz]

1st part, sub x=-3 in and then make entire eqn eql to 0 and for the second one sub x=-1 in a make eqn = 12. THen solve simultaneously

 

[pLuvia]

P(-3) = (-3)³ + 9a - 3b +6
= 9a - 3b - 21 = 0 ---------------------------- 1

P(-1) = (-1)³ + a - b + 6 = 12
= a - b = 7
a = 7 + b ---------------------------------------- 2

Sub a = 7 + b into eqn 1

9(7+b) - 3b - 21 = 0
63 + 9b - 3b - 21 = 0
42 + 6b = 0
b = -7
a = 0

 

[blackfriday]

P(-3)= 0

P(-3)=-27 + 9a - 3b + 6 = 0

9a - 3b = 21....(i)

P(-1) = 12

P(-1) = -1 + a - b + 6 = 12

a - b = 7....(ii)

3a - 3b = 21

(i) - 3(ii)

6a = 0

a = 0

b = -7

i bet ive made a silly mistake somewhere in there but its late and im off to 'powernap' haha

 

[YBK]

w00t w00t!

Thanks a lot guys

now i know what they meant with the remainder part.... i was actually almost half way there when I did the division transformation thingy...

great method though!!!

Thanks again!

p.s. I have MX1 exam on tuesday!!!!!!!!

 

[pLuvia]

What you still haven't had your yearlies how late is yours

 

[rnitya_25]

w00t w00t!

Thanks a lot guys

now i know what they meant with the remainder part.... i was actually almost half way there when I did the division transformation thingy...

great method though!!!

Thanks again!

p.s. I have MX1 exam on tuesday!!!!!!!!

maths ext1 is on thursday, revise your exam plan...

 

[pLuvia]

He's refering to his year 11 preliminaries

 

[YBK]

What you still haven't had your yearlies how late is yours

very late..!!


ARGGG... this past paper is HARD!!!!!!!!

Been doing other school's past papers and they're all so much easier... i'll post a few more questions I can't do in another thread.