Question

given that 2x-1 is a factor of P(x)=2x^3 + 3x^2 + 10x -6 , find the second factor of p(x)

Answer 1

2x^3 + 3x^2 + 10x -6 = (2x-1)(x^2 +2x +6)
-->the second factor is x^2 +2x +6

Answer 2

\[(2 x^3+3 x^2+10 x-6)/(2 x-1) =x^2+2 x+6\]

Answer 3

okay thanks..but how to show that second factor is always positive??

Answer 4

\[(b ^{2}-4ac)/2a\]

Answer 5

x^2 +2x +6= (x+1)^2 + 5 and this is positive for all x