Question

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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 :

$\large{\underline {\underline {\sf(\:1 \:)}}}$

• ${\sf{15x^2\:+\:52x\:+\:45}}$

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

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

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

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

$\large{\underline {\underline {\sf(\:2 \:)}}}$

• ${\sf{8x^2\:+\:26x\:+\:20}}$

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

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

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

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

$\large{\underline {\underline {\sf(\:3 \:)}}}$

• ${\sf{48x^2\:+\:14x\:+\:1}}$

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

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

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

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

$\large{\underline {\underline {\sf(\:4 \:)}}}$

• ${\sf{21x^2\:-\:x\:-\:2}}$

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

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

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

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

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

$\large{\underline {\underline {\sf(\:5 \:)}}}$

• ${\sf{8x^2\:-\:25x\:+\:18}}$

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

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

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

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

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

$\large{\underline {\underline {\sf(\:6 \:)}}}$

• ${\sf{15x^2\:-\:25x\:-\:40}}$

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

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

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

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

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

$\large{\underline {\underline {\sf(\:7 \:)}}}$

• ${\sf{45x^2\:+\:46x\:-\:63}}$

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

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

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

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

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

$\large{\underline {\underline {\sf(\:8 \:)}}}$

• ${\sf{81x^2\:+\:99x\:+\:28}}$

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

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

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

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

$\large{\underline {\underline {\sf(\:9 \:)}}}$

• ${\sf{6x^2\:-\:21x\:+\:9}}$

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

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

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

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

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

$\large{\underline {\underline {\sf(\:10 \:)}}}$

• ${\sf{20x^2\:-\:71x\:+\:63}}$

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

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

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

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

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

Answer 2

S O L U T Í O N :

① 15x² + 52x + 45

❭❭ 15x² + 52x + 45

❭❭ 15x² + 27x + 25x + 45

❭❭ 3x(5x + 9) + 5 (5x + 9)

❭❭ (3x + 5) or (5x + 9)

━━━━━━━━━━━━━━━━━━━━━━━━━━

② 8x² + 26x + 20

❭❭ 8x² + 26x + 20

❭❭ 8x² + 10x + 16x + 20

❭❭ 2x(4x + 5x) + 4 (4x + 5x)

❭❭ (2x + 4) or (4x + 5x)

━━━━━━━━━━━━━━━━━━━━━━━━━━

③ 48x² + 14x + 1

❭❭ 48x² + 14x + 1

❭❭ 8x² + 6x + 8x + 1

❭❭ 6x(8x + 1) + 1 (8x + 1)

❭❭ (6x + 1) or (8x + 1)

━━━━━━━━━━━━━━━━━━━━━━━━━━

④ 21x² - x - 2

❭❭ 21x² - x - 2

❭❭ 21x² - 7x - 6x - 2

❭❭ 7x(3x - 1) + 2 (3x - 1)

❭❭ (7x + 2) or (3x - 1)

━━━━━━━━━━━━━━━━━━━━━━━━━━

⑤ 8x² - 25x + 18

❭❭ 8x² - 25x + 18

❭❭ 8x² - 16x - 9x + 18

❭❭ 8x(x - 2) - 9 (x - 2)

❭❭ (8x - 9) or (x - 2)

━━━━━━━━━━━━━━━━━━━━━━━━━━

⑥ 15x² - 25x - 40

❭❭ 15x² - 25x - 40

❭❭ 15x² - 40x + 15x - 40

❭❭ 15x(x - 25) + 15 (x - 25)

❭❭ (15x + 15) or (x - 25)

━━━━━━━━━━━━━━━━━━━━━━━━━━

⑦ 45x² + 46x - 63

❭❭ 45x² + 46x - 63

❭❭ 45x² + 18x - 35x - 63

❭❭ 9x(5x + 9) - 7 (5x + 9)

❭❭ (9x - 7) or (5x + 9)

━━━━━━━━━━━━━━━━━━━━━━━━━━

⑧ 81x² + 99x + 28

❭❭ 81x² + 99x + 28

❭❭ 81x² + 63x + 36x + 28

❭❭ 9x(9x + 7) + 4 (9x + 7)

❭❭ (9x + 4) or (9x + 7)

━━━━━━━━━━━━━━━━━━━━━━━━━━

⑨ 6x² - 21x + 9

❭❭ 6x² - 21x + 9

❭❭ 6x² - 18x - 3x + 9

❭❭ 6x(x - 3) - 3 (x - 3)

❭❭ (6x - 3) or (x - 3)

━━━━━━━━━━━━━━━━━━━━━━━━━━

①⓪ 20x² - 71x + 63

❭❭ 20x² - 71x + 63

❭❭ 20x² - 36x - 35x + 63

❭❭ 4x(5x - 9) - 7 (5x - 9)

❭❭ (4x - 7) or ( 5x - 9)

━━━━━━━━━━━━━━━━━━━━━━━━━━