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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 - collecting like terms
a = 1b = 6c=11d=6

Answered by Rachel K. • Maths tutor

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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.

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