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The answer is A. x³ - x² - 17x + 12.
To multiply a binomial by a trinomial, we multiply each term in the first polynomial by each term in the second polynomial.
Multiplying the first term then the second term of the first polynomial by each term in the second polynomial, we now have
     (x+4)(x² - 5x + 3) = x³ - 5x² + 3x + 4x² - 20x + 12
Combining like terms to simplify and get the product equal to:
     (x+4)(x² - 5x + 3) = x³ - 5x² + 4x² + 3x - 20x + 12 
                                 = x³ - x² - 17x + 12

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