The polynomial is factored as y = (x + 3)(x - 3)(x - 4).
The polynomial given to us is : y = x³ - 4x² -9x + 36. We are given one of the factors of the polynomial. The factor is (x + 3). Now, we have to perform synthetic division to factorize the polynomial. We can rewrite the polynomial as : y = (x + 3)(x² -7x + 12). The second bracket can be further solved. The second bracket can be further solved as below :
B = x² -7x + 12 = x² - 4x - 3x + 12 = x(x - 4) -3(x - 4) = (x - 3)(x - 4)
So, the polynomial can be factored as y = (x + 3)(x - 3)(x - 4).
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