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If q(x)=x^2-5x+1, find : q(2+h)-q(2)/h

Sagot :

q(x) = x²-5x+1
q(2+h)-q(2)÷h
=[(2+h)²-5(2+h)+1]-[(2²-5(2)+1)÷h]
=[4+4h+h²-10-5h+1]-[(4-10+1)÷h]
=h²-h-5-(-5÷h)
=h²-h-5+(5/h)
=(h³-h²-5h+5)/h
=(h³-h²)-(5h+5)/h
=h²(h-1)-5(h+1)/h
=[(h²-5)(h-1)(h+1)]/h
=[(h²-5)(h²-1)]/h

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