Question

factorize the following equation
x⅔ + x⅓ - 6​

Answer 1

Answer:

This expression isn't even a polynomial, since polynomials are required to have whole-number exponents. However, this expression does have three terms, and the degree on the middle term is half of the degree on the leading term; and the third term is just a number. So this is in quadratic form; it's "a quadratic in x1/3". And, because the leading coefficient is just 1, this is actually a simple case of factoring.

I need factors of –6 that add to –1. I'll use –3 and +2 to split the middle term's coefficient. This gives me:

x2/3 – x1/3 – 6

(x1/3)2 – 1(x1/3) – 6

(x1/3 – 3)(x1/3 + 2)

There's nothing more that I can do with this, so I'm done. My answer is:

(x1/3 – 3)(x1/3 + 2)

Step-by-step explanation:

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