4x2-35x+49=(4x-7)(x-7). The giveaway is that 49 only has 2 pairs of factors: 49=1×49=7×7, which means that 7 could appear as the constant in the two factors. 4 has two pairs of factors: 4=1×4=2×2. The minus sign in the central term and the plus sign of the constant indicates that the constant is negative.
So we have 5 possibilities (4x-1)(x-49), (4x-49)(x-1), (4x-7)(x-7), (2x-7)(2x-7), (2x-49)(2x-1). Only one of these works (highlighted).