Polynomials

Algebra Level 4

If $x^5 - x^4 + x^3 - px^2 + qx + 4$ is divisible by both $(x+2)$ and $(x-1)$ , find the values of $-p$ and $-q$ respectively.

-12,-7 7,12 12,7 -7,-12

2 solutions

Sakanksha Deo
Mar 8, 2015

Since,

$x^{5} - x^{4} + x^{3} - px^{2} + qx + 4$

is divisible by (x + 2) and (x - 1)

Therefore,

$(-2)^{5} - (-2)^{4} + (-2)^{3} - p(-2)^{2} + qx + 4 = 0$

$2p + q = - 26$ ......... ( 1 )

Also,

$(1)^{5} -(1)^{4} + (1)^{3} - p(1)^{2} + qx + 4 = 0$

$p - q = 5$ ........... ( 2 )

By solving (1) and (2), we get,

p = -7 , q = -12

Why was this 100 points? This was easy $\ddot\smile$

Mehul Arora - 6 years, 2 months ago

Even I felt the same.This was very easy.

Sai Ram - 5 years, 11 months ago

the first equation is $2p+q=-26$

and second one is $p-q=5$

Rishabh Tripathi - 6 years, 2 months ago

Don't you think the question is a bit overrated? After all its just a simple remainder theorem question!!!

Aman Jain - 6 years, 2 months ago

Yeah It should be level 2 at maximum

Kushagra Sahni - 5 years, 11 months ago

@Kushagra Sahni – well... I'm not responsible for it. :D

Rishabh Tripathi - 5 years, 11 months ago

Shoham Grunblat
Apr 4, 2015

Just use horner's formula