Question

What should be subtracted to the polynomial $x^{2}-16x+30$, so that 15 is the zero of the resulting polynomial?
(a) 30
(b) 14
(c) 15
(d) 16

Answer 1

SOLUTION :  

The correct option is (c) : 15

A polynomial is exactly divisible by another polynomial, if remainder is zero. So , here find the remainder and subtract  remainder from f(x) , so that the resulting polynomial is divisible by g(x).

Given : f(x) = x² - 16x + 30

and one zero(x) = 15 ,  

So, x -15 is a factor of f(x)  

Therefore, g(x) = x - 15

Now on Dividing f(x) by g(x) , we get the following division process.  

      x - 15 )x² - 16x + 30( x -1

                  x² - 15x  

               (-)   (+)  

          ----------------------

                 - x + 30  

                 -x + 15  

              (+)  (-)  

         ------------------------

                       15  

Here, Remainder is 15 . Now the polynomial  f(x) = x² - 16x + 30 will be exactly divisible by g(x) = x - 15 when reminder is zero.  So to make the remainder 0 ,15 is to be subtracted from f(x) .  

Hence, if we subtract r(x) =  15 from  f(x) , then it will be divisible by g(x) =x - 15 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

p(x)=x2 -16x+30,

p(15)=152 -16*15+30

p(15)=225-240+30

p(15)=15

therefore 15 should be subtracted from p(x) so that 15 is the zero of the resulting polynomial