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let p be a polynomial p(x) = x^3+b*x^2+ c*x+24, where b and c are integers. Find a relation between b and c knowing that (x+2) divides p(x).

We know that (x+2) divides p(x), therefore p(x) can be written as p(x) = (x+2) q(x) + 0, where q is another polynomial of degree 2. We can calculate then p(-2): p(-2)= ((-2)+2) q(-2) = 0;p(-2)= (-2)^3+b (-2)...
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Answered by Tina-Alina S. • Maths tutor
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Find the radius and centre of the circle given x^2+4x+y^2+2y=20

Complete the square:x 2 +4x gives (x+2) 2 -4y 2 +2y gives (y+1) 2 -1Therefore,(x+2) 2 -4+(y+1) 2 -1=20Rearranging gives:(x+2) 2 +(y+1) 2 =25Comparing to the standard equation for a circle:(x-a) 2 +(y-b) 2 =r...
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Answered by Stanley C. • Maths tutor
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How can I find all the solutions to cos(3x) = sqrt(2)/2 for 0<=x<=2pi ?

Finding the solutions to trig equations begins in a very similar way to when we do it at GCSE. We start with:cos(2x) = 2 -1/2 0 &lt;= x &lt;=piand correct our range, as we are interested in 2x not just x: 0 ...
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Answered by Thomas U. • Maths tutor
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Finding the tangent of an equation using implicit differentiation

y 2 e 2x = 3y + x 2 1) Differentiation: Product rule, Explicity differentiation.2) Rearrangement: Collecting terms, Making dy/dx subject.
PJ
Answered by Paul J. • Maths tutor
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We are given y=(x^2)+3x-5. Find the derivative of y in terms of x.

From the question we have, y=x 2 +3x-5 The rule of differentiation, is that you take the power on the x and bring it to the front, leaving the power-1 behind. In other words if you have x n then the derivati...
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Answered by Maya B. • Maths tutor
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