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Factorise the expression $96 − 4 x − x 2$ .

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8 + x x + 12

8 − x x + 12

8 − x x − 12

None of these

answer is B.

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Detailed Solution

Given expression is

96 − 4 x − x 2

.
Rewrite the expression as

− x 2 + 4 x − 96

.
Using the identity,

x 2 + (a + b) x + a b = (x + a) (x + b)

Compare the expression with the identity and split the middle term,
Here,

(a + b) = 4

and

a b = − 96

.
So,

⇒ 12 − 8 = 4 ⇒ 12 × − 8 = − 96

So, the expression can be written as:

− x 2 + 4 x − 96 = − x 2 + 12 x − 8 x − 96 ⇒ − x 2 + 4 x − 96 = − x x + 12 − 8 x + 12 ⇒ − x 2 + 4 x − 96 = − x − 8 x + 12 ⇒ − x 2 + 4 x − 96 = 8 − x x + 12

Therefore, the factors of

96 − 4 x − x 2

are

8 − x x + 12

.
Hence, option 2 is correct.

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