Factorize:
$7 x^{2} + 49 x + 84$

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Solution

We have: $7 x^{2} + 49 x + 84 = 7 (x^{2} + 7 x + 12)$
We now have to split $7$ into two numbers such that their sum is $7$ and their product is $12.$
Clearly, $3 + 4 = 7$ and $3 \times 4 = 12.$
∴ $7 x^{2} + 49 x + 84$
$= 7 (x^{2} + 7 x + 12)$
$= 7 (x^{2} + 4 x + 3 x + 12)$
$= 7 [x (x + 4) + 3 (x + 4)]$
$= 7 (x + 4) (x + 3)$

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Similar questions

Which of the following is a factor of $(49 x^{2} - 1) + (1 + 7 x)^{2}$ ?

36 - 49 x^{2}

49 x^{2} - 36

49 x^{2} = 36

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