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p(x)=2x^3 + 7x^2 + 2x - 3. (a) Use the factor theorem to prove that x + 3 is a factor of p(x). (b) Simplify the expression (2x^3 + 7x^2 + 2x - 3)/(4x^2-1), x!= +- 0.5

(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(-3...
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Answered by James M. • Maths tutor
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There are a collection of CDs. There are 2 Rock CDs, x Pop CDs and 2x + 5 Jazz CDs. A CD is chosen at random, the probability that it is Rock is 1/20. Work out the probability it is Jazz.

To answer this question first we need to work out how many CDs we have in total. We do this by adding up the number of CDs in each category:Total = 2 + x + 2x + 5. We can simplify this to give:Total = 3x + 7...
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Answered by James M. • Maths tutor
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A circle is touching a square. The area of the square is 64 cm^2. Work out the area of the circle.

The first step of looking at a question like this is to highlight all the important information in the question. We are told that the square has an area of 64 cm 2 so what can we infer about the square based...
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Answered by James M. • Maths tutor
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Explain what is meant by a critical path.

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 time.
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Answered by George C. • Maths tutor
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Can you give an example of using the chain rule for differentiation? Example: Let y=(6 + 2x + 2x^2)^3, find dy/dx.

The chain rule is given by dy/dx= (dy/du)(du/dx). If we set u=6+2x+2x 2 then, y=u 3 thus, dy/dx=(3u 2 )(2+4x) = (3(6+2x+2x 2 ) 2 )(2+4x). Example does not ask to simplify expression or evaluate at any partic...
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Answered by Anthony H. • Maths tutor
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