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The polynomial p (x) = 2x^3+17x^2+41x+30 has a known factor of (x+5)

Rewrite p (x) as a product of linear factors

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  1. 10 July, 13:20
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    2x³ + 17x² + 41x + 30 = (x + 5) (x + 2) (2x + 3)

    Step-by-step explanation:

    2x³ + 17x² + 41x + 30 = (x + 5) (2x² + ax + 6) =

    2x³ + (a + 10) x² + (5a + 6) x + 30

    a + 10 = 17 a = 7 (check: 5a + 6 = 5 x 7 + 6 = 41)

    2x³ + 17x² + 41x + 30 = (x + 5) (2x² + 7x + 6) = (x + 5) (x + 2) (2x + 3)
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