Factorize-2 - 2-33 x-3

We have: 2x2+33x+3 We have to split nbsp;33 nbsp;into two numbers such that their sum is nbsp;33 nbsp;and their product is 6, i.e.,2 #215;3. Clearly, ...

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Standard IX

Mathematics

By Grouping

Factorize:2 ×...

Question

Factorize:
$2 x^{2} + 3 \sqrt{3} x + 3$

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Solution

We have:
$2 x^{2} + 3 \sqrt{3} x + 3$
We have to split $3 \sqrt{3}$ into two numbers such that their sum is $3 \sqrt{3}$ and their product is 6, i.e., $2 \times 3$ .
Clearly, $2 \sqrt{3} + \sqrt{3} = 3 \sqrt{3} and 2 \sqrt{3} \times \sqrt{3} = 6$ .

$∴ 2 x^{2} + 3 \sqrt{3} x + 3 = 2 x^{2} + 2 \sqrt{3} x + \sqrt{3} x + 3 = 2 x (x + \sqrt{3}) + \sqrt{3} (x + \sqrt{3}) = (x + \sqrt{3}) (2 x + \sqrt{3})$

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Factorize: 2x2+33x+3

We have: 2x2+33x+3 We have to split 33 into two numbers such that their sum is 33 and their product is 6, i.e.,2×3. Clearly, 23+3=33 and 23×3=6. ∴2x2+33x+3=2x2+23x+3x+3 =2xx+3+3x+3 =x+32x+3

Factorize:
$2 x^{2} + 3 \sqrt{3} x + 3$