The sum of $3$ expression is $8 + 13 a + 7 a^{2} .$ Two of them are $2 a^{2} + 3 a + 2$ and $3 a^{2} - 4 a + 1$ . Find the third expression.

a^{2} + a + 5

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2 a^{2} + a + 5

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2 a^{3} + 14 a + 5

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2 a^{2} + 14 a + 5

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Solution

The correct option is D $2 a^{2} + 14 a + 5$
Expression be x
$\Rightarrow x + (2 a^{2} + 3 a + 2) + (3 a^{2} - 4 a + 1)$ $= 8 + 13 a + 7 a^{2}$
$= x + 5 a^{2} - a + 3$ $= 8 + 13 a + 7 a^{2}$
$\Rightarrow x = 7 a^{2} + 13 a + 8 - 5 a^{2} + a - 3$
$x = 2 a^{2} + 14 a + 5$ .

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\frac{a^{2} - 16}{a^{3} - 8} \times \frac{2 a^{2} - 3 a - 2}{2 a^{2} + 9 a + 4} \div \frac{3 a^{2} - 11 a - 4}{a^{2} + 2 a + 4}

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