Question

What are the simplest factors of this polynomial? x3 + 4x2 – 9x – 36

Answer 1

(x-1) NO

(x-3) YES

(x+3) YES

(x-4) NO

(x+4) YES

Explanation:

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Answer 2

1. Factor out common terms in the first two terms, then in the last two terms:
x^2(x + 4) - 9(x + 4)
2. Factor out the common term x + 4
(x + 4)(x^2 - 9)
3. Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3
(x + 4)(x^2 - 3^2)
4. Use Difference of Squares: a^2 - b^2 = (a + b)(a - b)
(x + 4)(x + 3)(x - 3)