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3 years ago

Factor Completely: 12x2 + 22x + 6 A) (2x+ 3)(6x + 2) B) 6(x + 1)(2x + 1) C) 2(2x + 3)(3x + 1) D) 2(2x + 1)(3x + 3)

Mathematics

1 answer:

tia_tia [17]3 years ago

7 0

Answer:

C) 2 (2x + 3) (3x + 1)

Step-by-step explanation:

12x² + 22x + 6

2 ( 6x² + 11x + 3 )

2 [ 6x² + 9x + 2x + 3 ]

2 [ 3x ( 2x + 3 ) + 1 ( 2x + 3 ) ]

2 ( 2x + 3 ) ( 3x + 1 ) ⇒ C

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$3x + y = 6$

$y = - 3x + 6$

The coefficient of x is the slope of the line , So the slope of the above equation is -3 .

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Remember from now on ,

Product of multiplying the slopes of two lines which are perpendicular to each other , is -1 .

Thus ;

$( - 3) \times (m) = - 1$

m is the slope of the line which we want.

$- 3m = - 1$

Negatives simplifies

$3m = 1$

Divide sides by 3

$\frac{3m}{3} = \frac{1}{3} \\$

$m = \frac{1}{3} \\$

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We have following equation to find the point-slope form of the linear functions :

$y - y(0) = m(x - x(0))$

x(0) and y(0) are the coordinates of the point which the line passed through.

$y - 8 = \frac{1}{3} (x - 0) \\$

$y - 8 = \frac{1}{3} x \\$

Add sides 8

$y = \frac{1}{3} x + 8 \\$

Done....

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