How many ways can you rearrange the word FILTERS?

In the image, point a marks the center of the circle. which two lengths must form a ratio of 1 : 2? (options are in the images since thought they were harmful phrases)

Give all possible names for the line shown.calculation tip: lines can be written with either point first.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial