Apply division algorithm to find the quotient and remainder on dividing the polynomial 3 x^ + 4 x^ square + 6 x + 9 by x^ + 3x + 7 also verify the division algorithm

I suppose you mean

, and if we multiply by we get . Subtracting this from the numerator gives a remainder of .

, and multiplying by gives . Subtracting this from the previous remainder gives a new remainder of .

has no remaining factors of in it, so we're done, and

f is the midpoint of