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The first step in finding any turning point is to differentiate. To do this, we muiltiply x by its power and drop the power by 1. so in this senario we multiply the -2x by 2 giving us -4x and the power be...

(a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x).

The Factor Theorem is derived from the remainder theorem. We know from the remainder theorem that by doing p(x)/(x – a) then w...

A. t=0 ; x=250,000 B. 2020, so t=3. plug in to equation > x=250,000e^(0.012)3 = 259,163 (people so cannot round up) C. Population to double so 500,000 = 250,000e^(0.012)t -> 1/0.012(ln2) = t t= 57.7...

step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k ...

(i): 15x^(2)+7 --- in order to arrive at this answer, we can divide the equation into 3 separate parts: 5x^(3) and 7x and 3. For the first part, you would multiply the first number, 5 by the power, in thi...