0606 P21 - Nov 2017 - Q9 - 10 marks
8657
(i) Expand \((1+x)^4\), simplifying all coefficients.
(ii) Expand \((6-x)^4\), simplifying all coefficients.
(iii) Hence express \((6-x)^4-(1+x)^4=175\) in the form \(ax^3+bx^2+cx+d=0\), where \(a\), \(b\), \(c\), and \(d\) are integers.
(iv) Show that \(x=2\) is a solution of the equation in part (iii) and show that this equation has no other real roots.
