Polynomial question (1 Viewer)

[Joshmosh2]

P(x) is an even function and passes through the point (1,2). What is the remainder when P(x) is divided by (x+1)?

The possible answers were
a) 0
b) -1
c) 1
d) 2

What I thought was that since P(x) is an even function, P(-1) = P(1) so the answer is 1?
Not 100% sure about this one. Any help is greatly appreciated.

 

[seventhroot]

since it is an even function; it must have symmetry about the y axis but is there more to the question? it seems a little incomplete

this looks more MX1 to me

 

[faisalabdul16]

Question seems incomplete

 

[seventhroot]

Btw, I may have missed out some parts in the Q

niqqa

 

[Joshmosh2]

since it is an even function; it must have symmetry about the y axis but is there more to the question? it seems a little incomplete

this looks more MX1 to me

Oh I forgot, the polynomial passes through (1,2) .. LOL

 

[seventhroot]

Oh I forgot, the polynomial passes through (1,2) .. LOL

gg no re
the answer will be D

since P(-1) = P(1) as you said; it will have the same function value at x = - 1

 

[Kurosaki]

Oh I forgot, the polynomial passes through (1,2) .. LOL

D

 

[Joshmosh2]

Also, one more question.
This graph is f(x), so what would the gradient of the function look like?

http://imgur.com/9lUZrv4

 

[seventhroot]

Also, one more question.
This graph is f(x), so what would the gradient of the function look like?

http://imgur.com/9lUZrv4

It will look like y = ax^3

 

[emilios]

It will look like y = ax^3

Not quite. The function has 5 roots (notice the HPOI at the origin) so it will look more like a 'W' shaped quartic. The triple root at the origin becomes a double root when differentiated and the max and mins become roots of f'(x).

I got something that looks like this: http://www.wolframalpha.com/input/?i=y=50x^2(x-1)(x+1)

 

[Joshmosh2]

Not quite. The function has 5 roots (notice the HPOI at the origin) so it will look more like a 'W' shaped quartic. The triple root at the origin becomes a double root when differentiated and the max and mins become roots of f'(x).

I got something that looks like this: http://www.wolframalpha.com/input/?i=y=50x^2(x-1)(x+1)

Mine looked like that too. If the min of the function was placed much lower, for example like this: http://imgur.com/m8fDWP5
Would that correlate to a steeper part for that quartic?

 

[emilios]

Mine looked like that too. If the min of the function was placed much lower, for example like this: http://imgur.com/m8fDWP5
Would that correlate to a steeper part for that quartic?

Yes. Essentially the 'lower' placement of the min means the gradients of f(x) around the point are much larger i.e. the quartic will be steeper

 

[seventhroot]

Not quite. The function has 5 roots (notice the HPOI at the origin) so it will look more like a 'W' shaped quartic. The triple root at the origin becomes a double root when differentiated and the max and mins become roots of f'(x).

I got something that looks like this: http://www.wolframalpha.com/input/?i=y=50x^2(x-1)(x+1)

oops, I miscalculated 1+3+1 ._.

Essentially the graph "looks like" ax^5 so draw the derivative as bx^4