How do you factor this?

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How do you factor this?

$12 {(x + 2)}^{2} - 14 (x + 2) - 6$ $12(x+2)^2-14(x+2)-6$

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Answer 1 · 2017-12-15T04:05:09

$= 2 (2 x + 1) (3 x + 7)$ $=2(2x+1)(3x+7)$

Explanation:

let $(x + 2) = a$ $(x+2)=a$ for now.

$= 12 a^{2} - 14 a - 6$ $=12a^2-14a-6$ Factor out 2
$= 2 (6 a^{2} - 7 a - 3)$ $=2(6a^2-7a-3)$ Factor by grouping - Break middle term
$= 2 (6 a^{2} + 2 a - 9 a - 3)$ $=2(6a^2+2a-9a-3)$ Factor
$= 2 (2 a (3 a + 1) - 3 (3 a + 1))$ $=2(2a(3a+1)-3(3a+1))$ Factor out $(3 a + 1)$ $(3a+1)$
$= 2 (2 a - 3) (3 a + 1)$ $=2(2a-3)(3a+1)$

substitute $(x + 2)$ $(x+2)$ for $a$ $a$

$= 2 (2 (x + 2) - 3) (3 (x + 2) + 1)$ $=2(2(x+2)-3)(3(x+2)+1)$ Simplify by distribution
$= 2 (2 x + 4 - 3) (3 x + 6 + 1)$ $=2(2x+4-3)(3x+6+1)$ Add/Subtract
$= 2 (2 x + 1) (3 x + 7)$ $=2(2x+1)(3x+7)$
Done!

Lets test a value for fun.
for $x = 1$ $x=1$ ,
$= 12 {(1 + 2)}^{2} - 14 (1 + 2) - 6$ $=12(1+2)^2-14(1+2)-6$
$= 12 (9) - 14 (3) - 6$ $=12(9)-14(3)-6$
$= 108 - 42 - 6$ $=108-42-6$
$= 60$ $=60$

Now for the factored version.

$= 2 (2 (1) + 1) (3 (1) + 7))$ $=2(2(1)+1)(3(1)+7))$
$= 2 (3) (10)$ $=2(3)(10)$
$= 60$ $=60$

$60 = 60$ $60=60$ , $L S = R S$ $LS=RS$

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How do you factor this?

$12 {(x + 2)}^{2} - 14 (x + 2) - 6$ $12(x+2)^2-14(x+2)-6$

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you factor this?

12(x+2)2−14(x+2)−612(x+2)^2-14(x+2)-6

1 Answer

Explanation:

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Impact of this question

$12 {(x + 2)}^{2} - 14 (x + 2) - 6$ $12(x+2)^2-14(x+2)-6$