Answer:
5x³(2x -5)(2x +5)
2x+5 is a factor
Explanation:
You want the factorization of 20x⁵ -125x³.
Factors
We see immediately that x³ is a factor, and that both terms are divisible by 5. Factoring out 5x³ gives ...
= 5x³(4x² -25)
The factor in parentheses is a difference of squares, so that can be factored further:
= 5x³(2x -5)(2x +5) . . . . complete factorization
Of the listed factors, (2x+5) is a factor.
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Additional comment
The difference of squares is a special form that you see a lot in factoring problems. It is worthwhile to remember.
a² -b² = (a -b)(a +b)
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