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If P(x)= 3x^4 - 5x^3 - 17x^2 + 13x + 6, and P(1)=0, and P(-2)=0, then the factorization of P(x) is?

Respuesta :

Answer:

P(x) = (x - 1)(x + 2)(x - 3)(3x + 1)

Step-by-step explanation:

Since P(1) = 0 and P(- 2) = 0, then

(x - 1) and (x + 2) are factors of P(x)

(x - 1)(x + 2) = x² + x - 2 ← is also a factor of P(x)

dividing 3[tex]x^{4}[/tex] - 5x³ - 17x² + 13x + 6 by x² + x - 2 gives

P(x) = (x - 1)(x + 2)(3x² - 8x - 3) = (x - 1)(x + 2)(x - 3)(3x + 1)


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