Polynomiall help (1 Viewer)

[darkphoenix]

I was doing excel ext2 and there was a step that i don't really get:
P(x)= (x-2)(x-3)Q(x)+5x-6
then P(x) is divided by (x-2)(x-3) then remainder is 5x-6

how does that work please explain. Thanks

 

[AAEldar]

 

[SpiralFlex]

You haven't asked a specific question.

The form you have shown is the division identity statement.



In short,



So your remainder would be in this case,

 

[darkphoenix]

OH right, ok, I was thinking about the remainder theorem in the last step. Now is pretty easy Thx
Anyway, if you guys want practice this is the question(x) is divided by x-2 and x-3, the respective remainders are 4 and 9. Find the remainder when P(x) is divided by (x-2)(x-3).

 

[darkphoenix]

lol, nice

 

[SpiralFlex]

Let




Let



Now,




Hence the remainder is,

 

[Carrotsticks]

Also something to note, is that if we divide P(x) by a quadratic, the remainder (if there is one) can be expressed as a linear factor ax+b. However, this does NOT mean that it HAS to be linear. The remainder could just be a constant, or even 0.

Similarly, if I were to divide P(x) by a cubic, then my remainder can be expressed as ax^2 + bx + c. Just like the above, it doesn't HAVE to be a quadratic. It could be quadratic, linear, constant, or 0.

Following this trend, if I were to divide a polynomial by another polynomial of degree N, then the remainder can be expressed as another polynomial of degree N-1.

This is the reason why Spiral chucked a 'ax+b' as his remainder, in case you were wondering.

BTW obviously, this is assuming that the power of P(x) is greater than the power of the divisor.

 

[darkphoenix]

Great, I got that. Ty