Question

plz tell the ans of this Q.

Answer 1

Answer:

Proof-

Step-by-step explanation:

x²+3x+2

x²+2x+x+2

x(x+2)+(x+2)

(x+1)(x+2)

Since x²+3x+2 will divide the given polynomial, therefore, x+1 and x+2 should also divi6the polynomial.

Using Remainder theorm,

putting x+1=0=>x=-1 in polynomial,

2(-1)⁴+(-1)³-14(-1)²-19(-1)-6

2-1-14+19-6

21-21

0, hence x+1 is a factor of polynomial

Now, putting x+2=0=>x=-2 in polynomial,

2(-2)⁴+(-2)³-14(-2)²-19(-2)-6

32-8-56+38-6

70-70

0, hence x+2 is a factor of polynomial

=>x²+3x+2 divides the polynomial completely.