Question

what must be added to polynomial 2x3+9x2-5x-15 so that the resulting polynomial is exactly divisible by 2x+3

Answer 1

2x+3)2x³+9x²-5x-15(x²+3x-7
2x³+3x²
- -
-------------
6x²-5x-15
6x²+9x-15
-. -
---------------
-14x-15
-14x-15
+ +
-------------
0

Answer 2

Answer:

-6 must be added to the polynomial $2x^{3}+9x^{2}-5x-15$ so that the resulting polynomial is exactly divisible by $2x+3$

Step-by-step explanation:

Given polynomial is P(x)= $2x^{3}+9x^{2}-5x-15$

Let a is the number which must be added to above polynomial so that it is exactly divisible by 2x+3

So, by remainder theorem

P($\frac{-3}{2}$) + a = 0

⇒  $2(\frac{-3}{2})^{3}+9(\frac{-3}{2})^{2}-5(\frac{-3}{2})-15+a=0$

⇒   $\frac{-27}{4}+\frac{81}{4}+\frac{-15}{2}+a=0$

⇒   6+a=0 ⇒ a = -6

Hence, -6 must be added to the polynomial $2x^{3}+9x^{2}-5x-15$ so that the resulting polynomial is exactly divisible by 2x+3