[4 marks sum]

Question 14 Marks

Divide$: 36a^3x^5 − 24a^4x^4 + 18a^5x^3$ by $− 6a^3x^3.$

Answer

$36 a^3 x^5-24 a^4 x^4+18 a^5 x^3 \text { by }-6 a^3 x^3$
$=\frac{36 a^3 x^5-24 a^4 x^4+18 a^5 x^3}{-6 a^3 x^3}$
$=\frac{36 a^3 x^5}{-6 a^3 x^3}-\frac{24 a^4 x^4}{-6 a^3 x^3}+\frac{18 a^5 x^3}{-6 a^3 x^3}$
$=-6 a^{3-3} \cdot x^{5-3}+4 a^{4-3} \cdot x^{4-3}-3 a^{5-3} \cdot x^{3-3}$
$=-6 a^0 x^2+4 a^1 x^2-3 a^2 x^0$
$=-6 x^2+4 a c-3 a^2 \ldots \ldots \ldots \ldots . .\left(\because x^0 \text { or } y^0=1\right)$

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Question 24 Marks

Divide $: 15x^3y^2 + 25x^2y^3 − 36x^4y^4$ by $5x^2y^2$

Answer

$15 x^3 y^2+25 x^2 y^3-36 x^4 y^4 \text { by } 5 x^2 y^2$
$=\frac{15 x^3 y^2+25 x^2 y^3-36 x^4 y^4}{5 x^2 y^2}$
$=\frac{15 x^3 y^2}{5 x^2 y^2}+\frac{25 x^2 y^3}{5 x^2 y^2}-\frac{36 x^4 y^4}{5 x^2 y^2}$
$=3 x^{3-2} \cdot y^{2-2}+5 x^{2-2} \cdot y^{3-2}-\frac{36}{5} x^{4-2} \cdot y^{4-2}$
$=3 x^1 y^0+5 x^0 y^1-\frac{36}{5} x^2 y^2$
$=3 x+5 y-\frac{36}{5} x^2 y^2 \ldots \ldots \ldots . .\left(\because x^0 \text { or } y^0=1\right)$

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Question 34 Marks

Simplify: $2 \frac{2}{3} x y-3 \frac{1}{2} x y+3 \frac{1}{3} x y-2 \frac{1}{2} x y$

Answer

$2 \frac{2}{3} x y-3 \frac{1}{2} x y+3 \frac{1}{3} x y-2 \frac{1}{2} x y$
$=x y\left(2 \frac{2}{3}-3 \frac{1}{2}+3 \frac{1}{3}-2 \frac{1}{2}\right)$
$=x y\left(\frac{8}{3}-\frac{7}{2}+\frac{10}{3}-\frac{5}{2}\right)$
$=x y\left(\frac{16-21+20-15}{6}\right)$
$=x y\left(\frac{36-36}{6}\right)$
$=0 \times x y$
$=0$

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MATHS [4 marks sum]

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