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anonymous

  • 4 years ago

how to factor this binomial? 25x^2+1

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  1. anonymous
    • 4 years ago
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    (-i+5 x) (i+5 x)

  2. asnaseer
    • 4 years ago
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    \[a^2+b^2=(a+ib)(a-ib)\]

  3. Mertsj
    • 4 years ago
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    That is the sum of two squares and it is prime within the set of real numbers.

  4. Mertsj
    • 4 years ago
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    What class are you taking?

  5. anonymous
    • 4 years ago
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    algebra...

  6. Mertsj
    • 4 years ago
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    So have you had imaginary numbers yet?

  7. anonymous
    • 4 years ago
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    no

  8. Mertsj
    • 4 years ago
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    Then put down that this binomial cannot be factored and is prime.

  9. Mertsj
    • 4 years ago
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    If it were the difference of two squares, it would be factorable but since it is the sum of two squares, it is prime.

  10. anonymous
    • 4 years ago
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    so what's the difference of sum/diff of squares?

  11. Mertsj
    • 4 years ago
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    x^2 is a square 16 is a square x^+16 is the sum of two squares and cannot be factored x^2-16 is the difference of two squares and can be factored.

  12. Mertsj
    • 4 years ago
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    Sum means add. Difference means subtract.

  13. anonymous
    • 4 years ago
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    so whenever there is a - sign it can be factored and when + is prime?

  14. Mertsj
    • 4 years ago
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    Yes. If those signs join two squares.

  15. asnaseer
    • 4 years ago
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    Mertsj: why do say this must be prime? (e.g. when x=1, we get \(25x^2+1=26\) which is not a prime number.

  16. Mertsj
    • 4 years ago
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    Prime means has no factors except itself and 1

  17. asnaseer
    • 4 years ago
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    so mean the "expression" is prime rather than the number that it produces?

  18. Mertsj
    • 4 years ago
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    Yes

  19. asnaseer
    • 4 years ago
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    ok - thx for clarifying

  20. Mertsj
    • 4 years ago
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    5 is prime

  21. Mertsj
    • 4 years ago
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    x^2+4 is prime

  22. Mertsj
    • 4 years ago
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    yw

  23. anonymous
    • 4 years ago
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    got you!!!

  24. Mertsj
    • 4 years ago
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    Good

  25. Directrix
    • 4 years ago
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    x^2 + 4 is a prime expression over the set of Reals but is not prime over the set of Complex numbers.

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