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Express the polynomial as a product of linear factors.
1x) = 3x^3+12x^2 + 3x - 18
O A. (x-2)(x+3)(x-3)
O B. (x+3)(x + 6)(x - 1)
O c. 3(x - 1)(x+3)(x+2)
D. (x-3)(x + 3)(x - 2)

Express the polynomial as a product of linear factors 1x 3x312x2 3x 18 O A x2x3x3 O B x3x 6x 1 O c 3x 1x3x2 D x3x 3x 2 class=

Respuesta :

Answer:

C

Step-by-step explanation:

Given

3x³ + 12x² + 3x - 18

The sum of the coefficients = 3 + 12 + 3 - 18 = 0

Thus x = 1 is a root and (x - 1) is a factor

Divide 3x³ + 12x² + 3x - 18 by (x - 1) using Synthetic division

 1 |  3   12   3   - 18

       ↓   3   15     18  

    -----------------------------

       3   15   18     0 ← remainder

Quotient = 3x² + 15x + 18 = 3(x² + 5x + 6)

Thus

3x³ + 12x² + 3x - 18 = 3(x - 1)(x² + 5x + 6) = 3(x - 1(x + 3)(x + 2) → C

   

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