When I saw '98,' my very first thought was that 98=2*49 and 49 is a perfect square. Thus, rewrite 98-2x^2 as 2(49-x^2). 49-x^2 is the "difference of two squares," and there is a formula for factoring it: a^2 - b^2 = (a - b)(a + b).
Thus, 2(49-x^2) = 2(7-x)(7+x)