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Factorise the expression $28 − 31 x − 5 x 2$ .

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x + 7 4 − 5 x

x − 7 4 − 5 x

x + 7 4 + 5 x

None of these

answer is A.

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Detailed Solution

Given expression is

28 − 31 x − 5 x 2

.
This can be rewritten as:

28 − 31 x − 5 x 2 = − 5 x 2 + 31 x − 28

To factorise the given expression, taking the product of the coefficient of

x 2

with the constant term where constant term is 28 and coefficient of

is 5,

⇒ 5 × 28 = 140

Now, finding the factors of

140

and treat them as the coefficient of x.

⇒ 140 = 35 × 4

Now, subtracting the factors,

⇒ 35 − 4 = 31

So, the expression can be written as:
Question Image

Therefore, the factors of the given expression are

x + 7 and 4 − 5 x

.
Thus, the factorisation of

.
Hence, option 1 is correct.

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