The method of solution is Long division
[tex]\frac{4x^2+14x+16}{x+2}[/tex]This should be written as
[tex]x+2\sqrt[]{4x^2+14x+16}[/tex]Then, divide the first term i.e 4x² by x and write the answer at the top, multiply the result and subtract as you can see in the image below.
Hence the quotient=4x+6, remainder = 4