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Answer:

(x-3)(x+3)(x+4)

explaination:

To factor the polynomial x + 4x^2 - 9x - 36, we first rearrange it to standard form: 4x^2 - 8x - 36. We can apply the Rational Root Theorem to find possible rational roots, which include ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, and ±36. Testing these values, we find that x = 3 is a root. We can then use synthetic division or long division to factor out (x - 3), resulting in 4x^2 - 8x - 36 = (x - 3)(4x + 12). The quadratic can be further factored as (x + 3)(x + 4). Therefore, the completely factored form of the polynomial is (x - 3)(x + 3)(x + 4).

Topic: Algebra, Polynomial Factoring

Tags: algebra polynomials factoring rational roots

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What is the completely factored form of x + 4x^2 - 9x - 36?

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