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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...
JM
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...
AH
Answered by Anthony H. • Maths tutor
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Find the equation of the normal to the curve at the point (1, -1 ): 10yx^2 + 6x - 2y + 3 = x^3

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-y 1 =m(x-x 1 ) can be used to find its equation. We are given...
TD
Answered by Tutor125302 D. • Maths tutor
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Express x^2-4x+9 in the form (x-p)^2+q where p and q are integers

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 similarities such as the x^2 term a...
MN
Answered by Mark N. • Maths tutor
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