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प्रश्न
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
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उत्तर
\[\text{We have to find the value of a if} (x + 2) \text{is a factor of} (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a) . \]
\[\text{Substituting}\ x = - 2\ \text{in}\ 4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a, \text{we get:} \]
\[4( - 2 )^4 + 2( - 2 )^3 - 3( - 2 )^2 + 8( - 2) + 5a = 0\]
\[or, 64 - 16 - 12 - 16 + 5a = 0\]
\[or, 5a = - 20\]
\[or, a = - 4\]
\[ \therefore If (x + 2) \text{is a factor of}\ (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a), a = - 4 . \]
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Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 14x2 + 13x − 15 | 7x − 4 |
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| Dividend | Divisor |
| 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
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