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Answer :
Final answer:
In this case, the greatest common factor is `x⁴⁰` and the factored expression is `5x² + 40x - 45`.
Explanation:
To factorize the expression `5x⁶ + 40x⁵ - 45x⁴`, we first need to identify the greatest common factor (GCF) that can be factored out from each term. In this expression, one can observe that each term is divisible by `x⁴`. This indicates that `x⁴` is a common factor.
Therefore, our first step will be to factor out `x⁴` from each term:
- 1. Factor out `x⁴` from 5x⁶, which will give `5x²`.
- 2. Factor out `x⁴` from 40x⁵, which will give `40x`.
- 3. Factor out `x⁴` from -45x⁴, which will give `-45`.
After factoring `x^4` from each term, the expression becomes `5x² + 40x - 45`.
Therefore, the factored version of expression `5x⁶ + 40x⁵ - 45x⁴` is `x⁴(5x² + 40x - 45)`.
Hence, the GCF is `x⁴` and the factored expression is `5² + 40x - 45`.
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