Question

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

Answer 1

$\bold{\red{Question}}$

Show that (x + 1)(x + 2)(x+3) can be written in the form ax3 + bx? + cx + d

where a, b, c and d are positive integers.

Solution

lets expand the first two brackets first,

so x * x gives x2,

x * 2 gives 2x,

x * 1 gives x

and 1 * 2 = 2

2x and x are both in terms of x so we add these together to get 3x,

giving us the quadratic (x2 + 3x + 2).

now we expand this bracket with (x +3). x2 * x = x3x2 * 3 = 3x2 3x * x = 3x2 3x * 3 = 9x 2 * x = 2x 2 * 3 = 6

then when we add all the like terms together

we get

x3+ 6x2+ 11x + 6

so

a=1, b=6, c=11 and d= 6

hope it helps ☺️