Question

Please help me by solving this​

Answer 1

F A C T O R S. O F :

• 1. ${\sf{15x^2\:+\:52x\:+\:45}}$

• 2. ${\sf{8x^2\:+\:26x\:+\:20}}$

• 3. ${\sf{48x^2\:+\:14x\:+\:1}}$

• 4. ${\sf{21x^2\:-\:x\:-\:2}}$

• 5. ${\sf{8x^2\:-\:25x\:+\:18}}$

• 6. ${\sf{15x^2\:-\:25x\:-\:40}}$

• 7. ${\sf{45x^2\:+\:46x\:-\:63}}$

• 8. ${\sf{81x^2\:+\:99x\:+\:28}}$

• 9. ${\sf{6x^2\:-\:21x\:+\:9}}$

• 10. ${\sf{20x^2\:-\:71x\:+\:63}}$

E X P L A N A T I O N :

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:1 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{15x^2\:+\:52x\:+\:45}}$

${\sf{15x^2\:+\; \bigg(25x\:+\:27x\bigg)\:+\:45}}$

${\sf{5x\; \bigg(3x\:+\:5\bigg)\;+\:9\; \bigg(3x\:+\:5\bigg)}}$

${\sf{\bigg(5x\:+\:9\bigg)\; \bigg(3x\:+\:5\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:2 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{8x^2\:+\:26x\:+\:20}}$

${\sf{8x^2\:+\; \bigg(10x\:+\:16x\bigg)\:+\:20}}$

${\sf{2x\; \bigg(4x\;+\;5x\; \bigg)\:+\:4\; \bigg(4x\;+\;5x\; \bigg)}}$

${\sf{\bigg(2x\:+\;4\bigg)\; \bigg(4x\;+\:5x\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:3 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{48x^2\:+\:14x\:+\:1}}$

${\sf{8x^2\:+\; \bigg(6x\:+\:8x\bigg)\:+\:1}}$

${\sf{6x\:+\; \bigg(8x\:+\:1\bigg)\;+\;1}}$

${\sf{\bigg(6x\:+\:1\bigg)\; \bigg(8x\:+\;1\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:4 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{21x^2\:-\:x\:-\:2}}$

${\sf{21x^2\:-\; \bigg(7x\:-\:6x\bigg)\:-\:2}}$

${\sf{21x^2\:-\;7x\:+\:6x\:-\:2}}$

${\sf{7x\; \bigg(3x\:-\:1\bigg)\:+\:2\; \bigg(3x\;-\;1\bigg)}}$

${\sf{\bigg(7x\:+2\bigg)\; \bigg(3x\:-\:1\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:5 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{8x^2\:-\:25x\:+\:18}}$

${\sf{8x^2\:-\; \bigg(16x\:+\:9x\bigg)\:+\;18}}$

${\sf{8x^2\:-\:16x\:-\:9x\:+\:18}}$

${\sf{8x\; \bigg(x\:-\:2\bigg)\:-\:9\; \bigg(x\:-\:2\bigg)}}$

${\sf{\bigg(8x\:-\:9\bigg)\; \bigg(x\:-\:2\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:6 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{15x^2\:-\:25x\:-\:40}}$

${\sf{5x^2\:-\; \bigg(40x\:-\:15x\bigg)\:-\:40}}$

${\sf{15x^2\:-\:40x\:+\:15x\:-\:40}}$

${\sf{15x\; \bigg(x-\:25x\bigg)\:+\:15\; \bigg(x\:-\:25\bigg)}}$

${\sf{\bigg(15x\:+\;15\bigg)\; \bigg(x\:-\:25\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:7 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{45x^2\:+\:46x\:-\:63}}$

${\sf{45x^2\:+\; \bigg(18x\:-\:35x\bigg)\:-\:63}}$

${\sf{45x^2\:+\;18x\:-\:35x\:-\:63}}$

${\sf{9x\; \bigg(5x\:+\;9\bigg)\:-\:7\; \bigg(5x\:+\:9\bigg)}}$

${\sf{\bigg(9x\; +\:4\bigg)\; \bigg(9x\:+\:7\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:8 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{81x^2\:+\:99x\:+\:28}}$

${\sf{81x^2\:+\; \bigg(63x\:+\:36x\bigg)\:+\:28}}$

${\sf{9x\; \bigg(9x\:+\:7\bigg)\;+\;4\; \bigg(9x\:+\:7\bigg)}}$

${\sf{\bigg(9x\:+\:4\bigg)\; \bigg(9x\:+\:7\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:9 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{6x^2\:-\:21x\:+\:9}}$

${\sf{6x^2\:-\; \bigg(18x\:+\:3x\bigg)\:+\:9}}$

${\sf{6x^2\:-\;18x\:-\:3x\:+\:9}}$

${\sf{6x\; \bigg(x\:-\;3\bigg)\:-\:3\; \bigg(x\:-\:3\bigg)}}$

${\sf{\bigg(6x\:-\;3\bigg)\; \bigg(x\:-\:3\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:10 \:)}}}\\\end{gathered}\end{gathered}$

• ${\sf{20x^2\:-\:71x\:+\:63}}$

${\sf{20x^2\:-\; \bigg(36x\:+\:35x\bigg)\:+\:63}}$

${\sf{20x^2\:-\;36x\:-\:35x\:+\:63}}$

${\sf{4x\; \bigg(5x\:-\;9\bigg)\:-\:7\; \bigg(5x\:-\:9\bigg)}}$

${\sf{\bigg(4x\:-\;7\bigg)\; \bigg(5x\:-\:9\bigg)}}$

$~~~~~~~~~~~~~~$ _______________________

$~~~~$$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Proved!}}}}$

$~~~~~~~~~~~~~~$ _______________________

Answer 2

Answer:

Hi Shivani

Are you tamil ??