Dividing $2 x^{2} + 13 x + 15$ by $x + 5$ and then substituting $x = 2$ in the resulting expression gives
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Solution

$2 x^{2} + 13 x + 15 = 2 x^{2} + 10 x + 3 x + 15 = 2 x (x + 5) + 3 (x + 5) = \frac{(2 x + 3) (x + 5)}{(x + 5)} = 2 x + 3$

Substituting $x = 2$ in resulting expression gives $2 \times 2 + 3 = 7$ .

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2 x^{2} + 13 x + 15

x + 5

3 x^{3} + 2 x^{2} + 13 x + 42

(x + 2)

Find and correct the errors in the following mathematical statement. Substituting x = −3 in

(a) x² + 5x + 4 gives (−3)² + 5 (−3) + 4 = 9 + 2 + 4 = 15

(b) x² − 5x + 4 gives (−3)² − 5 (−3) + 4 = 9 − 15 + 4 = −2

Substituting $x = - 3$ in $x^{2} + 5 x$ gives $3^{2} + 5 (- 3) = - 9 - 15 = - 24.$

\frac{2 x^{2} + 13 x + 15}{x^{2} + 3 x - 10} \div \frac{2 x^{2} - x - 6}{x^{2} - 4 x + 4}

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