Prove that for all whole values of n the value of the expression:
n(n–1)–(n+3)(n+2) is divisible by 6.

Explanation:

Multiply it out.

n^2 -n -(n^2 +5n+6)

= -6n -6

= -6(n +1)

For any integer value of n, this is divisible by 6. (The quotient is -(n+1).)

160

step-by-step explanation:

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step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)