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प्रश्न
Factorize each of the following algebraic expression:
40 + 3x − x2
उत्तर
We have:
\[40 + 3x - x^2 \]
\[ \Rightarrow - ( x^2 - 3x - 40) \]
\[\text{ To factorise }( x^2 - 3x - 40),\text{ we will find two numbers p and q such that }p + q = - 3\text{ and pq }= - 40 . \]
Now,
\[5 + ( - 8) = - 3 \]
and
\[5 \times ( - 8) = - 40\]
\[\text{ Splitting the middle term }- 3x \text{ in the given quadratic as }5x - 8x,\text{ we get: }\]
\[40 + 3x - x^2 = - ( x^2 - 3x - 40)\]
\[ = - ( x^2 + 5x - 8x - 40)\]
\[ = - [( x^2 + 5x) - (8x + 40)]\]
\[ = - [x(x + 5) - 8(x + 5)]\]
\[ = - (x - 8)(x + 5)\]
\[ = (x + 5)( - x + 8)\]
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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 |
