# Adding Multiples of Consecutive Odd Numbers by Mathematical Induction

(a) Factorise \( 4x^3 + 18x^2 + 23x + 9 \). \( \begin{align} \displaystyle 4x^3 + 18x^2 + 23x + 9 &= 4x^3 + 4x^2 + 14x^2 + 23x + 9 \\ &= 4x^2 (x+1) + 14x^2 + 14x + 9x + 9 \\ &= 4x^2 (x+1) + 14x(x+1) + 9(x+1) \\ &= (x+1)(4x^2 [...]