.If x2 + kx+ 6 = (x + 2) (x + 3) for all x, then the value of k is

k = 5

Step-by-step explanation:

Now comparing left hand side & right hand side ,

Cancelling x^2 & 6 from both left hand side & right hand side ,

kx = 5x

=> k = 5

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1