3+23z 8z^2 =3+24z z 8z^2 ∵ 3× ( 8)= 24 ∴ 24= 24× ( 1) 23=24 1 =3(1+8z) z(1+8z) =(1+8z)(3 z) ...

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Factorisation by Regrouping Terms

Factorise: 3+...

Question

Factorise:

$3 + 23 z - 8 z^{2}$

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Solution

$3 + 23 z - 8 z^{2} = 3 + 24 z - z - 8 z^{2} ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 3 \times (- 8) = - 24 ∴ - 24 = - 24 \times (- 1) 23 = 24 - 1 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ = 3 (1 + 8 z) - z (1 + 8 z) = (1 + 8 z) (3 - z)$

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