Question

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

Answer 1

Answer:

-6

Step-by-step explanation:

the factor is x=-3/2

2 x (-3/2)^3 + 9 x (-3/2)^2 + 5x(-3/2) - 15+k=0

so u get -27/4 x +81/4 +15/2-15=-k

so -27+81+30-60=-4k

24=-4k

k=-6

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:

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

Solution :

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 $2x+3$

By remainder theorem,

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

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

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

$6+a=0$

$a =-6$

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