1. ## Polynomial Quesiton

1) When the polynomial 3x^3+ax^2+bx-9 is divided by x-2, the remainder is -5. When it is divided by x+1, the remainder is -16. Determine the values of a and b.

2) Determine the values of m and n so that the polynomial 2x^3+mx^2+nx-3 and x^3-3mx^2+2nx+4 are both division by x-2.

Help PLease? and show full solution if you possiblely can...

2. Originally Posted by Rarrazz
1) When the polynomial 3x^3+ax^2+bx-9 is divided by x-2, the remainder is -5. When it is divided by x+1, the remainder is -16. Determine the values of a and b.

$P(2) = 3(2)^3+a(2)^2+b(2)-9 = -5$

and

$P(-1) = 3(-1)^3+a(-1)^2+b(-1)-9 = -16$

Can you solve this system?

3. Originally Posted by pickslides
$P(2) = 3(2)^3+a(2)^2+b(2)-9 = -5$

and

$P(-1) = 3(-1)^3+a(-1)^2+b(-1)-9 = -16$

Can you solve this system?
huh? yaa i know how to do that,
but there i are 2 unknown varaible in the equations, a and b
i just dont know how to get rid one...

well...

3(2)^3+a(2)^2+b(2)-9 = -5
24+2a+2b-9 = -5
15+2a+2b = -5
2a+2b = -20
a+2b = -10
a+b = -5

3(-1)^3+a(-1)^2+b(-1)-9 = -16
-3+a-b-9 = -16
a-b-12 = -16
a-b = -4

now im stuck...

4. Originally Posted by Rarrazz

a+b = -5

a-b = -4

now im stuck...

$a+b = -5$ ...(1)
$a-b = -4$ ...(2)

(1) - (2) gives

$2b = -1 \Rightarrow b = \dfrac{-1}{2}$

Can you finish it?

5. Originally Posted by pickslides
$a+b = -5$ ...(1)
$a-b = -4$ ...(2)

(1) - (2) gives

$2b = -1 \Rightarrow b = \dfrac{-1}{2}$

Can you finish it?
sorry, i dont quite understand, can you please explain...

6. I used these equations from your working above

$a+b = -5$ ...(1)
$a-b = -4$ ...(2)

I have labelled them (1) and (2)

Now saying (1) - (2) cancels out the a

leaving $b-(-b) = 2b$

and $-5-(-4) = -1$

making those equal

$2b = -1 \Rightarrow b = \dfrac{-1}{2}$

You can use this to find a.

7. Originally Posted by pickslides
I used these equations from your working above

$a+b = -5$ ...(1)
$a-b = -4$ ...(2)

I have labelled them (1) and (2)

Now saying (1) - (2) cancels out the a

leaving $b-(-b) = 2b$

and $-5-(-4) = -1$

making those equal

$2b = -1 \Rightarrow b = \dfrac{-1}{2}$

You can use this to find a.
if you are saying like this,

P(2) = 3(2)^3 + A(2)^2 - 1/2(2) - 9 = -5

i tried to figure out a but it is different, the answer from my text book is different...

8. Originally Posted by Rarrazz
if you are saying like this,

P(2) = 3(2)^3 + A(2)^2 - 1/2(2) - 9 = -5
You should use

$b = \dfrac{-1}{2}$

for

$a+b = -5$

$a+\dfrac{-1}{2} = -5$

can you solve for a?

9. Originally Posted by Rarrazz
2a+2b = -20
a+2b = -10
a+b = -5
what happened here?

it is like this

2a+2b = -20
2(a+b) = -20
a+b = -10

Originally Posted by Rarrazz
3(2)^3+a(2)^2+b(2)-9 = -5
24+2a+2b-9 = -5
somethings gone wrong here aswell

a(2)^2=4a not 2a