Px=xsquare+7x+9is divided by gx ,we get (x+2)and -1 as quetient and remainder respectively .find gx

Px=xsquare+7x+9is divided by gx ,we get (x+2)and -1 as quetient and re

1.	Px=xsquare+7x+9is divided by gx ,we get (x+2)and -1 as quetient and remainder respectively .find gx
Answer» Quadratic equation, p(x) = x2 + 7x + 9Quotient, q(x) = x + 2Remainder, r(x) = - 1Divisor, g(x) = ?p(x) = g(x) q(x) + r(x)x2+ 7x + 9 = g(x) (x + 2) - 1x2+7x+9+1 = g(x) (x+2)\xa0x2+7x+10 = g(x) (x+2){tex}\\therefore{/tex}\xa0g(x) =\xa0{tex}\\frac { x ^ { 2 } + 7 x + 10 } { x + 2 }{/tex}g(x) =\xa0{tex}\\frac {x^2+2x+5x+10}{x+2}{/tex}g(x) =\xa0{tex}\\frac {x(x+2)+5(x+2)}{x+2}{/tex}{tex}= \\frac { ( x + 2 ) ( x + 5 ) } { ( x + 2 ) }{/tex}g(x) = x + 5