The polynomial g(x) = 3x³ + 11x² - 14x - 40 as the product of linear factors is g(x) = (3x + 5)(x - 2)(x + 4)
Rewriting the polynomial g(x) as the product of linear factors.
From the question, we have the following parameters that can be used in our computation:
g(x) = 3x³ + 11x² - 14x - 40
3x + 5
Using the long division method, we have
x² + 2x - 8
3x + 5 | 3x³ + 11x² - 14x - 40
3x³ + 5x²
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6x² - 14x - 40
6x² + 10x
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-24x - 40
-24x - 40
--------------------------------------------------
0
So, we have
g(x) = 3x³ + 11x² - 14x - 40 = (3x + 5)(x² + 2x - 8)
When factored we have
g(x) = 3x³ + 11x² - 14x - 40 = (3x + 5)(x - 2)(x + 4)
Hence, the polynomial g(x) as the product of linear factors is g(x) = (3x + 5)(x - 2)(x + 4)