Concept:Expressing numbers in base x as polynomials in powers of x allows the subtraction to be solved algebraically.Explanation:Given: 6244x−1621x=4323x.Write each number in expanded base x form:6244x=6x3+2x2+4x+41621x=x3+6x2+2x+14323x=4x3+3x2+2x+3Subtract the left side:(6x3+2x2+4x+4)−(x3+6x2+2x+1)=5x3−4x2+2x+3Equate this to 4323x:5x3−4x2+2x+3=4x3+3x2+2x+3Bring all terms to one side:x3−7x2=0x2(x−7)=0Since x is a valid base, x=0. Therefore, x=7.Answer:x=7, which means the base is Seven.