Question

2n^2 - n - 190 = 0 factorize​

Answer 1

Answer:

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Answer 2

Given: An expression $2n^{2} -n - 190 = 0$

To find: The factorized form of the given expression

Solution: The given expression is:

$2n^{2} -n - 190 = 0$

Using middle term splitting method:

Step 1: We need to split the middle term (-$n$) in such a way that the product of the splitted terms is -$380n^{2}$ [2$n^{2}$ * (-190)] and addition is -$n$.

∵ $2n^{2} - 20n + 19n - 190 = 0$                                                                                             [$-20n + 19n = -n$ and $-20n \ * \ 19n = -380n^{2}$]

Step2: Take out the common factors.

⇒ $2n(n-10) + 19(n -10) = 0$

Step 3: Take $(n-10)$ common from both the terms

⇒ $(n-10)(2n + 19) = 0$

Step 4: Compare both the terms with 0.

⇒ $n -10 =0 \ or \ 2n+19= 0$

⇒ $n = 10 \ or \ n =\frac{-19}{2}$

Hence, the factorized form of the given expression is $(n-10)(2n + 19) = 0$ and factors are $n = 10 \ or \ n =\frac{-19}{2}$.