Show that (x+2)(x+3)(x+4) can be written in the form of ax^3+bx^2+cx+d where a, b, c and d are positive integers.
This is a 'show that' question which means that you need to prove that something is true. This question wants you to rewrite (x+2)(x+3)(x+4) into the form of ax^3+bx^2+cx+d. To do this, we have to expand the original formula. It is much easier to do this in two steps rather than expand the formula in one step.So we start with the first two. (x+2)(x+3)(x+4)=(x2+2x+3x+6)(x+4)=(x2+5x+6)(x+4)So now we only have two brackets to expand. We start by multiplying everything in the first bracket by x and then by 4.= (x3+ 5x2+ 6x + 4x2 +20x + 24)We simplify this by adding together numbers with the same coefficient.= (x3 + 9x2 + 26x + 24)so expanded the formula is now x3 + 9x2 + 26x + 24.This has successfully taken the form of ax3 +bx2 + cx + d.a=1, b=9, c=26 and d=24.
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