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6x^3+11x^2-4x-4 divide the polynomial

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Answer: (x + 2)(3x - 2)(2x + 1)

Explanation:

First, find the possible rational roots. Then use synthetic division (or long division) to find a root. Next, factor the reduced polynomial.

6x³ + 11x² - 4x - 4

P = 4: ± 1, 2, 4

Q = 6: ± 1, 2, 3

Possible rational roots are: ± {1, 2, 4,
(1)/(2), (1)/(3), (2)/(3), (4)/(3)}

Try x = -2 --> which is the factor (x + 2)

-2 | 6 11 -4 -4

| ↓ -12 2 4

6 -1 -2 0 ← Remainder of 0 means (x + 2) is a factor

The reduced polynomial is:

6x² - 1x - 2

Factors of (6)(-2) = -12

1 -12 = -11

2 -6 = -4

3 -4 = -1 this works!

Replace -1x with +3x - 4x and use the grouping method to factor:

6x² + 3x -4x -2

3x(2x + 1) -2(2x + 1) So the factors are: (3x - 2) and (2x + 1)

User Ariets
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