A polynomial, h(t) = 2t - at + bt + 4 represents Mr. Bill's height in metres at 't seconds. "-Mr." Bill is rapidly approaching a tall brick wall which is 100 metres high and will reach the wall in 3 seconds. "-You" need to find out if Mr. Bill will clear the wall (pass over it) or slam into it! Oh, → h(t) = 2t at + bt+4 has a remainder of 9 when divided by (t-1) and a remainder of "-36" when divided by (t+2).
a) What Theorem do you have to use to answer this question? Explain why.
b) b) Now, find the values of 'a' and 'b'. Make sure that you show ALL of your work. Include a BRIEF explanation of each step.
c) Now, will Mr. Bill make it over the wall or is he plasticine chunky salsa?