If f(x) is divisible by 2x+3, then f(x+1) is divisible by?

Question

anonymous · Answer

2x + 5? hehe just guessing

callisto · Answer

i forgot, I just suddenly remember this type of question and I cannot solve it..

anonymous · Answer

1

anonymous · Answer

2(x+1) + 3 ?

anonymous · Answer

From the given information,

f(x) = (2x+3) Q(x) so, f(x+1) = (2x+5) Q(x+1)

anonymous · Answer

So, Ishaan is right.

apoorvk · Answer

Yeah Ishaan, I would have guessed the same.

callisto · Answer

Alright , i don't understand.
What about if f(x) is divisible by x-1, which of the following must be a factor of f(2x+1) ?
A. x 
B . x-3
C. 2x-1
D. 2x+1
This time.. I've got the answer for this one , but i don't know how to solve it

anonymous · Answer

A

anonymous · Answer

same method.

anonymous · Answer

Let $ f (x) = (x - 1) Q (x)$, then $$ f (2x + 1) = (2x + 1 - 1) Q (2x + 1)= 2x Q (2x + 1) $$

Hence x is a factor of f (2x + 1).

(Ans: A)

callisto · Answer

Oh this time i understand, thanks!!!

anonymous · Answer

I am glad you did.

anonymous · Answer

Time for the problem of the day guys! ;)

callisto · Answer

right, for the first one i don't understand
i thought
f(x) = (2x+3) Q(x) 
 f(x+1) = (2x+3 +1) Q(x+1) = 2(x+1) Q(x+1) ?

mani_jha · Answer

When you find f(x+1), you just substitute x+1 instead of x. No other changes in that. Just like to find f(2) you substitute 2 instead of x.
So f(x+1)={2(x+1)+3)Q(x+1)
={2x+2+3}Q(x+1)
=(2x+5)Q(x+1)
Ok?

callisto · Answer

Yup, thanks a ton!