Factorize the following by using splitting the middle term x2+2x-3 .

# Factorize the following by using splitting the middle term ${x}^{2}+2x-3$ .

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

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### Solution:

The given polynomial is ${x}^{2}+2x-3.$
Comparing the given polynomial with $a{x}^{2}+\mathit{bx}+c$ we get,
where, $a=1,b=2,c=-3$.
Here $=\left(1\right)\left(-3\right)=-3$ , so we try to split $b=2$ into two parts whose sum is 2 and product is -3.
Therefore, possible factors are and 1, 1 and -3.
Clearly, pair -1 and 3 gives $-1+3=2=b$.
$={x}^{2}+\left(-1+3\right)x-3$ $=\left(x-1\right)\left(x+3\right)$ Thus, the factors of ${x}^{2}+2x-3$ , by using splitting the middle term are $\left(x-1\right)\left(x+3\right)$ .
Therefore, option 2 is correct.

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