Question

Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

Answer 1

okay I will show you:

Answer 2

thank you so much!

Answer 3

:(

Answer 4

thinking

Answer 5

oh ok sorry

Answer 6

sorry, it too late for me I will hand this over to lonesome else?

Answer 7

ok

Answer 8

thanks anyways

Answer 9

Here it goes~
Have you learnt remainder theorem yet?

Answer 10

@pottersheep Are you there??

Answer 11

Yes sorry, we have!

Answer 12

So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?

Answer 13

ok one sec

Answer 14

So i'd sub in 2 for x

Answer 15

Yup!

Answer 16

3?

Answer 17

sorryryyryryryr

Answer 18

Sorry what do I do with the b though?

Answer 19

4b -24

Answer 20

Right, so for p(2), you get p(2) = 4b - 24 = R, agree?
(By remainder theorem, p(a) = R , when p(x) is divided by x-a)

Answer 21

Right, okay

Answer 22

And what is the remainder when p(x) is divided by x+1 ?

Answer 23

b - 5

Answer 24

Not really..
Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?

Answer 25

Opps, sorry! I subbed in 1!

Answer 26

9??

Answer 27

b + 9!

Answer 28

Yes.
Note that the remainder is p(x) = R when p(x) is divided by x-a.
Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]

Answer 29

True, sorry!

Answer 30

From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?

Answer 31

Oh.. It's okay!

Answer 32

Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!

Answer 33

Yes. Since they have the SAME remainder!
You're welcome :)