Question

Factor x^4 – 3x^3 – 3x^2 + 7x + 6 completely, given that 2 and 3 are zeros.

(x + 2)(x + 3)(x + 1)^2

(x + 2)(x + 3)(x^2 + 2x + 1)

(x – 2)(x – 3)(x + 1)

(x – 2)(x – 3)(x + 1)^2

Answer 1

Since 2 and 3 are zeros, (x − 2)(x − 3) is a factor. Divide:

(x^4 − 3x^3 − 3x^2 + 7x + 6) ÷ (x^2 − 5x + 6) = x^2 + 2x + 1 = (x + 1)^2.

Thus the complete factorization is (x − 2)(x − 3)(x + 1)^2.