$9 x^{2} + 18 x + 8$ factorize it.

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Solution

To factorize $9 x^{2} + 18 x + 8$ split the middle terms
$= 9 x^{2} + 12 x + 6 x + 8$
( Split the middle term in such a way that the Sum of the split terms should be equal to the middle terms ( $12 x + 6 x = 18 x$ ) and its product should be equal to the product of the coefficient of $x^{2}$ and constant term $12 \times 6 = 9 \times 8 = 72$ )
$= 3 x (3 x + 4) + 2 (3 x + 4)$ ( Take $3 x$ common from $9 x^{2}$ $a n d$ $12 x$ and $2$ from $6 x a n d 8$ )
$= (3 x + 4) (3 x + 2)$ ( Write common factor once and other factors together )
Hence, the factors of $9 x^{2} + 18 x + 8$ are $(3 x + 4) (3 x + 2)$ .

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