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(a) The factor theorem states that: the polynomial f(x) has a factor (x - a) if and only if f(a) = 0.Use that information, we know that (x + 3) is a factor of p(x) if p(-3) = 0. So let's test it:p(-3) = 2...

The critical path is the path from the start to the end event continuously, with the end of one activity forming the start of the next. There is zero float and the project will be completed in the minimum...

The chain rule is given by dy/dx= (dy/du)(du/dx). If we set u=6+2x+2x²then, y=u³ thus, dy/dx=(3u²)(2+4x) = (3(6+2x+2x²)²)(2+4x). Example does not ask...

Firstly, an expression for dy/dx needs to be found to allow us to find the gradient of the normal. As a normal is a straight line, the equation y-y₁=m(x-x₁) can be used to find its e...

The first step would be to expand the second equation:(x-p)^2+qx^2-px-px+p^2+q

this simplifies to x^2-2px+p^2+q

After this you examine the two equations and identify their similariti...