Factorize  2×2+35x+5 by splitting the middle term.

# Factorize  $2{x}^{2}+3\sqrt{5}x+5$ by splitting the middle term.

1. A
$\left(2x+\sqrt{5}\right)\left(x-\sqrt{5}\right)$
2. B
$\left(2x-\sqrt{5}\right)\left(x+\sqrt{5}\right)$
3. C
$\left(2x+\sqrt{5}\right)\left(x+\sqrt{5}\right)$
4. D
$\left(2x-\sqrt{5}\right)\left(x-\sqrt{5}\right)$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

The given polynomial is $2{x}^{2}+3\sqrt{5}x+5.$
Comparing the given polynomial with $a{x}^{2}+\mathit{bx}+c$ we get,
where, $a=2,b=3\sqrt{5},c=5$ .
Here $\mathit{ac}=\left(2\right)\left(5\right)=10$  , so we try to split   into two parts whose sum is $3\sqrt{5}$and the product is 10.
Therefore, possible factors are 2$\sqrt{5}$and$\sqrt{5}$, -2$\sqrt{5}$and-$\sqrt{5}$.
Clearly, pair 2$\sqrt{5}$and$\sqrt{5}$ gives $2\sqrt{5}+\sqrt{5}=3\sqrt{5}=b$.
$=2{x}^{2}+\left(2\sqrt{5}+\sqrt{5\right)}x+5$
$=2{x}^{2}+2\sqrt{5}x+\sqrt{5}x+5$
$=2x\left(x+\sqrt{5\right)}+\sqrt{5\left(}x+\sqrt{5}\right)$
$=\left(2x+\sqrt{5}\right)\left(x+\sqrt{5}\right)$ Thus, the factors of $2{x}^{2}+3\sqrt{5}x+5$ , by using splitting the middle term are.
Therefore, option 3 is correct.

## Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)