Number System
Aptitude

 Back to Questions
Q.

What number should be subtracted from $x^3+ 4x^2- 7x + 12$, if it is to be perfectly divisible by $x + 3$?

 A.

42

 B.

39

 C.

13

 D.

None of these

 Hide Ans

Solution:
Option(A) is correct

According to remainder theorem when $dfrac{f(x)}{x+a}$, then the remainder is $f(-a)$.

In this case, as $x + 3$ divides $x^3 + 4x^2 - 7x + 12 – k$ perfectly ($k$ being the number to be subtracted), the remainder is 0 when the value of $x$ is substituted by -3.

i.e., $(-3)^3 + 4(-3)^2 - 7(-3) + 12 - k = 0$

or $-27 + 36 + 21 + 12 = k$

or $k =$ 42


(1) Comment(s)


Chandresh
 ()

hi,

In the above question, how you have taken value of x as -3. by solving it or randomly.

can u please elaborate.

Thanking you...