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16. Factor completely 20x^5 - 125x³. Which of the following is one of the factors?

O (x+5)
O (2x + 5)
O5x5
O(x - 5).

User Stanton
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1 Answer

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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.

__

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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User Doon
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