Question

For what value of k is the polynominal 21'+ 4 + 2x + 3x + 6 exactly divisible by (x + 2) ?​

Answer 1

Step-by-step explanation:Let p(x) = 2x  

4

+3x  

3

+2px  

2

+3x+6

By factor theorem, p(x) will be exactly divisible by (x+2) if $$p ( -2) = 0.Now,p(-2) = 2( -2)^4 + 3( -2)^3 + 2p( -2)^2 + 3( -2) + 6= 32 - 24 + 8p - 6 + 6= 8 + 8p$$

Since,  p(−2)=0

⇒8+8p=0

⇒8p=0

⇒8p=−8

⇒p=−1