# Determine m and n if 3x^2-x-2 is a factor of the polynomial 3x^4+mx^3-19x^2+nx+12. Express in factored form.?

### 2 Answers

- ?Lv 73 weeks agoFavourite answer
If 3x² - x - 2 is a quadratic factor the we can say:

(3x² - x - 2)(ax² + bx + c) = 3x⁴ + mx³ - 19x² + nx + 12

By inspection we see that a = 1 and c = -6 so,

(3x² - x - 2)(x² + bx - 6) = 3x⁴ + mx³ - 19x² + nx + 12

Equating coefficients of x³ and x² we have:

3b - 1 = m and -20 - b = -19

so, b = -1

Hence, m = -4

Then, with coefficients of x we have:

6 - 2b = n

so, n = 8

Then, (3x² - x - 2)(x² - x - 6) = 3x⁴ - 4x³ - 19x² + 8x + 12

i.e. (3x² - x - 2)(x - 3)(x + 2)

or, (3x + 2)(x - 1)(x - 3)(x + 2)

:)>

- rotchmLv 73 weeks ago
Hints:

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