Factorize: $4 z^{2} - 8 x + 3$
$(a) (2 z - 1) (2 z - 3)$
$(b) (2 z + 1) (3 - 2 z)$
$(c) (2 z + 3) (3 z - 1)$
$(d) (z - 1) (4 z - 3)$

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Solution

The correct option is (a): $(2 z - 1) (2 z - 3)$
Given: $4 z^{2} - 8 x + 3$
Using Middle term splitting method,
$\Rightarrow 4 z^{2} - 6 z - 2 z + 3$
$\Rightarrow 2 z (2 z - 3) - 1 (2 z - 3)$
$\Rightarrow (2 z - 1) (2 z - 3)$
$∴ 4 z^{2} - 8 x + 3 = (2 z - 1) (2 z - 3)$

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