Question

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40 marks allotted for 4 questions
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Answer 1

$\begin{aligned}1. &\Longrightarrow\ 4x^3+5x+2x^5-9\\ \\ &\Longrightarrow\ 2x^5+4x^3+5x-9\\ \\ &\Longrightarrow\ 2x^5+6x^4-6x^4-18x^3+22x^3+66x^2-66x^2-198x+203x+609-618\\ \\ &\Longrightarrow\ 2x^4(x+3)-6x^3(x+3)+22x^2(x+3)-66x(x+3)+203(x+3)-618\\ \\ &\Longrightarrow\ (x+3)(2x^4-6x^3+22x^2-66x+203)-618\end{aligned}$

$\begin{aligned}2. &\Longrightarrow\ 9x^5+4x^3+3x+2\\ \\ &\Longrightarrow\ 9x^5+4x^3+18x-15x+2\\ \\ &\Longrightarrow\ 9x^5+18x+4x^3-15x+2\\ \\ &\Longrightarrow\ 9(x^5+2x)+4x^3-15x+2\end{aligned}$

$\displaystyle \begin{aligned}3. &\Longrightarrow\ 9a^3-8a^2+7a-6\\ \\ &\Longrightarrow\ 9a^3+6a^2-14a^2-9\frac{1}{3}a+16\frac{1}{3}a+10\frac{8}{9}-16\frac{8}{9}\\ \\ &\Longrightarrow\ 3a^2(3a+2)-4\frac{2}{3}a(3a+2)+5\frac{4}{9}(3a+2)-16\frac{8}{9}\\ \\ &\Longrightarrow\ (3a+2)\left(3a^2-4\frac{2}{3}a+5\frac{4}{9}\right)-16\frac{8}{9}\end{aligned}$

$\begin{aligned}4. &\Longrightarrow\ 60a^2-60+4a^2\\ \\ &\Longrightarrow\ 64a^2-60\\ \\ &\Longrightarrow\ 64a^2+32a-32a-16-44\\ \\ &\Longrightarrow\ 8a(8a+4)-4(8a+4)-44\\ \\ &\Longrightarrow\ (8a+4)(8a-4)-44\\ \\ \\ &OR\\ \\ \\ &\Longrightarrow\ 60a^2-60+4a^2\\ \\ &\Longrightarrow\ 64a^2-60\\ \\ &\Longrightarrow\ 64a^2-16-44\\ \\ &\Longrightarrow\ [64a^2-16]-44\\ \\ &\Longrightarrow\ (8a+4)(8a-4)-44\ \ \ \ \ [\because\ a^2-b^2=(a+b)(a-b)]\end{aligned}$

Answer 2

Answer:

Step-by-step explanation: