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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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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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What's the difference between the Imperfect and Preterite tense?

The Imperfect tense is primarily used for explaining actions that happened regularly in the past or for explaining characteristics and states of things in the past. For example, you would say 'había mucho ca...
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Answered by Imogen F. • Spanish tutor
2706 Views

When do I use the subjunctive in Spanish?

The subjunctive is a mood, not a tense. The other ‘moods’ would be the indicative and the imperative. The subjunctive also exists in English (“If I were rich, I would…”) but it is much more common in Spanish...
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Answered by Jasmine K. • Spanish tutor
2376 Views

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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