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We must use the factor theorem since that is what the question asks. So we take p(x) and think about the factors of 8 we then evaluate it at x=1 to start, then move onto x=-1,2,-2 and so on. We see that i...

The general formula for integration by parts is given as
∫u(dv/dx)dx = uv - ∫v(du/dx)dx
given that the equation to be solved is ∫x²sin2xdx, the values for u, v, du/dx and dv/dx can ...

First of all, when we expand brackets we know that the x will be at the start of the brackets 

(x    )(x    )= 0

Look a the equation again, x²+5x+6=0. All of our numbers are posit...

52,724 53,000 We round up because 7 is greater than 5 and is therefore closer to 10 than 0.

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by appl...