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The Brainliest Answer!
  • Brainly User
2016-07-08T00:35:25+08:00
Y = 9x³ + 36x² - 4x - 16

Factor by grouping:

(9x³ + 36x²) + (-4x - 16)

9x² (x + 4) - 4(x + 4)

(9x² - 4) (x + 4)

Factor further 9x² - 4 ⇒ (3x + 2) (3x - 2)

ANSWER:  The factors are (x+4) (3x +2) (3x- 2)

From these factors, you can now solve for the roots of the polynomial:

y = 9x³ + 36x² - 4x + 6

y = (x + 4) (3x + 2) (3x - 2)

Set y to 0:

x + 4 = 0         3x + 2 = 0           3x - 2 = 0
x = -4              3x = -2               3x = 2
                       3x/3 = -2/3         3x/3 = 2/3
                       x = -2/3             x = 2/3

The roots/solution are: -4,  -2/3,   2/3
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