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Why is (x^3 - 7x^2 +13x - 6) divisible with (x-2)?

If we look at the general form a polynom P(X) divides Q(x) if and only if Q(x) = P(x) * T(x).Assume P(x) = a n x n + a n-1 x n-1 + ... + a 1 x + a 0 . How do the roots of P(x) relate to the roots of Q(x), wh...
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Answered by Vlad-Mihai E. • Maths tutor
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Complete the square for x^2 + x - 6.

First, let us separate the constant term and complete the square for (x^2 + 1x). x^2 + x - 6 = (x^2 + x) - 6 Now, let us halve the coefficient of x. 0.5 of +1 = +0.5 Write (x )^2 with half the coefficient of...
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Answered by Larra T. • Maths tutor
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Factorise fully the following: x^2 + 7x + 10.

Think S ir P aul M cCartney. ( SPM ) The S symbolises the square in the first section, the P means think of two numbers which plus to make 7 and the M means think of two numbers which multiply to make 10. If...
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Answered by Keighley H. • Maths tutor
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A level Maths question - The graph of y=2sin(2x)+1 is rotated 360 degrees about the x-axis to form a solid. Find the volume enclosed by the curve, the co-ordinate axes and the line x=pi/2

First, recall that the formula for finding such a volume is pi times the integral from 0 to pi/2 of y^2 with respect to x. This leads to pi times the integral from 0 to pi/2 of 4sin^2(2x) + 4sin(2x) + 1 (thi...
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Answered by Robbie K. • Maths tutor
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Prove the identity: (cos θ + sin θ)/(cosθ-sinθ) ≡ sec 2θ + tan 2θ

First rewrite right hand side in terms of sinθ and cosθ, because those are the terms we'll be dealing with on the left hand side: sec2θ+tan2θ = 1/cos2θ + sin2θ/cos2θ, so RHS = (1+sin2θ)/cos2θNow look at the ...
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Answered by Margot M. • Maths tutor
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