For the following frequency distribution and taking suitable scales on both the axes, draw a histogram.

Use the graph drawn to estimate the value of the mode.

If 2x³ + ax² + bx - 6 has a factor (2x + 1) and leaves a remainder 12 when divided by (x + 2). Calculate the values of a and b hence factorise the given expression completely.

Points A, B and C divide the line segment joining the points D(8, -4) and E(-12, 16) in four equal parts. Find the equation of the line that passes through point A and is perpendicular to DE.