Question

If 3x^2+11x+10=(3x+5)(x+k) then k =___​

Answer 1

GIVEN,

$3x^2+11x+10=(3x+5)(x+k)$

TO FIND,

The value of $k$.

SOLUTION,

It is given that $3x^2+11x+10=(3x+5)(x+k)$, by simplifying the bracket on the Right Hand Side, we get  $3x^2+11x+10=3x^2+3kx+5x+5k$.  Further simplifying the equation,

$3x^2 - 3x^2 +11x-5x+10=3kx+5k$,

$6x+10=3kx+5k$,

Taking $k$ as common on the right-hand side we get,

$6x+10=k(3x+5)$,

$(6x+10)/(3x+5)=k$

$2=k$

Hence If $3x^2+11x+10=(3x+5)(x+k)$ then k = 2.