Which of the following is equal to $(x + 2) (x + 3) ?$

$x^{2} + 5 x + 6$

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$x^{2} + 4 x + 6$

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$x^{2} + 3 x + 6$

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$x^{2} + 2 x + 6$

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Solution

The correct option is A
$x^{2} + 5 x + 6$

We know that:

$(x + a) (x + b) = x^{2} + x (a + b) + a b$

$\Rightarrow (x + 2) (x + 3) = x^{2} + x (2 + 3) + 2 \times 3$

$\Rightarrow (x + 2) (x + 3) = x^{2} + 5 x + 6$

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lim x \to \infty \frac{2 \sqrt{x} + 3 \sqrt[3]{x} + 4 \sqrt[4]{x} + . . . + n \sqrt[n]{x}}{\sqrt{(2 x - 3)} + \sqrt[3]{(2 x - 3)} + \sqrt[4]{(2 x - 3)} + . . . + \sqrt[n]{(2 x - 3)}}

Which of the following is equal to $(x + 2) (x + 3) ?$

\int \frac{(x + 2) d x}{\sqrt{(x - 2) (x - 3)}}

\frac{2 x}{3} + 1 = \frac{7 x}{15} + 3

x

(2 x + 3 y)^{2}

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