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प्रश्न
Factorize each of the following algebraic expression:
x2 − 4x − 21
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उत्तर
\[\text{ To factorise }x^2 - 4x - 21,\text{ we will find two numbers p and q such that }p + q = - 4\text{ and }pq = - 21 . \]
Now,
\[3 + ( - 7) = - 4 \]
and
\[3 \times ( - 7) = - 21\]
\[\text{ Splitting the middle term }- 4x\text{ in the given quadratic as }- 7x + 3x, \text{ we get: }\]
\[ x^2 - 4x - 21 = x^2 - 7x + 3x - 21\]
\[ = ( x^2 - 7x) + (3x - 21)\]
\[ = x(x - 7) + 3(x - 7)\]
\[ = (x + 3)(x - 7)\]
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Factorise the following expression.
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The value of p in the equation `(2"p")/3` = 10 is ________
Match the following :
| Column A | Column B |
| (a) `x/2` = 10 | (i) x = 4 |
| (b) 20 = 6x − 4 | (ii) x = 1 |
| (c) 2x − 5 = 3 − x | (iii) x = 20 |
| (d) 7x − 4 − 8x = 20 | (iv) x = `8/3` |
| (e) `4/11 - x = (-7)/11` | (v) x = −24 |
