Factorize: $x^{2} + 6 x + 8$

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Solution

Comparing $x^{2} + 6 x + 8$ with $x^{2} + (a + b) x + a b = (x + a) (x + b)$ ,
we get $a b = 8$ and $a + b = 6$ .
$∴ x^{2} + 6 x + 8 = x^{2} + (2 + 4) x + (2 \times 4)$
$= (x + 2) (x + 4)$
The factors of $x^{2} + 6 x + 8$ are $(x + 2)$ and $(x + 4)$ .
Factors of $8$ Sum of factors
$1, 8$ $9$
$2, 4$ $6$
Hence the correct factors are $2, 4$

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