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Show that (x + 1)(x + 2)(x + 3) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are positive integers.

(x+1)(x+2) = ( x^2 + 3x + 2) - multiplying out the first 2 terms(x^2 + 3x + 2)(x + 3) = x^3 + 3x^2 + 2x + 3x^2 + 9x + 6 - multiplying the product of the first two terms by the last termx^3 + 6x^2 + 11x + 6 -...
RK
Answered by Rachel K. • Maths tutor
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Define the concept of the “procedural” and the “declarative” memory according to Cohen's theory about long term memory, and explain how the two concepts differ from each other.

LTM (long term memory) can be divided into the declarative (explicit) memory and the procedural (implicit) memory. The procedural memory is nonverbal in nature and is responsible for our motor skills. It con...
SL
Answered by Sarah L. • Psychology tutor
3779 Views

Integrate exp(2x)cos(8x) by parts

Let u=exp(2x) and v'=cos(8x)From these you can obtain u' and vu=2exp(2x) and v=1/8 sin(8x)Formula: integral(uv'dx)=uv-integral(vu'dx)=1/8 exp(2x)sin(8x)-integral(1/4 sin(8x)exp(2x))=1/8exp(2x)sin(8x)+1/16cos...
CD
Answered by Chloe D. • Maths tutor
3994 Views

Solve the equation 8x^6 + 7x^3 -1 = 0

The first thing to recognise is this is a quadratic in disguise, therefore we can rewrite the equation in terms of a new variable y. Where y=x 3 The equation then becomes 8y 2 +7y-1=0 . We then factorise thi...
KP
Answered by Kelan P. • Maths tutor
8337 Views

What is the best way to do well in my Italian GCSE oral exam?

Firstly, make sure you are aware of the topics your exam board uses in speaking exams, e.g. 'school', 'holidays' or 'hobbies' and commit to learning some key vocab for each topic. For example, if you're aske...
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Answered by Violetta K. • Italian tutor
6490 Views