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anonymous

  • one year ago

What are the roots of the polynomial equation x^4+x^3=4x^2+4x? –2, –1, 0, 2 –2, 0, 1, 2 –1, 0 0, 1

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  1. freckles
    • one year ago
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    you could write everything on one side and try to factor

  2. welshfella
    • one year ago
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    x^4+x^3=4x^2+4x x^4 + x^3 - 4x^2 - 4x = 0 take out the common factor x x(x^3 + x^2 - 4x - 4) = 0 so what is one root?

  3. welshfella
    • one year ago
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    when two expression are multiplied and the result is zero then either one = zero right?

  4. anonymous
    • one year ago
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    yes, so it would be D?

  5. welshfella
    • one year ago
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    dont jump to conclusions all we can say is that x = 0 one root is 0

  6. welshfella
    • one year ago
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    - so it could be any of the 4 options now we can look to see if we can factor the cubic in the parentheses

  7. welshfella
    • one year ago
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    x^3 + x^2 - 4x - 4 = 0

  8. welshfella
    • one year ago
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    we can factor this by grouping can you factor the first 2 terms x ^3 and x^2 - what is the highest common factor of these 2?

  9. welshfella
    • one year ago
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    what is the highest thing which divides into x^3 and x^2?

  10. welshfella
    • one year ago
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    is it x or is it x^2?

  11. anonymous
    • one year ago
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    it would be x^2

  12. welshfella
    • one year ago
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    yes so it factors to x^2(x + 1) OK with that?

  13. anonymous
    • one year ago
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    yes

  14. welshfella
    • one year ago
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    right so so far we have x^1(x + 1) - 4x - 4 = 0 it would be nice if we could get another (x + 1) so we could factor further and we can do this by taking out -4 from the lat 2 terms so we get x^2( x + 1) - 4(x + 1) = 0 taking out the x+ 1 (x^2 - 4)(x + 1) = 0 do you follow that ok?

  15. anonymous
    • one year ago
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    sure do :)

  16. welshfella
    • one year ago
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    great so now we have x^2 - 4 = 0 and x + 1 = 0 x = 2 , -2 and -1 so final answer is 2, -2, -1 and 0

  17. welshfella
    • one year ago
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    A is correct

  18. anonymous
    • one year ago
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    Thank you for explaining this to me!!!

  19. welshfella
    • one year ago
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    yw

  20. welshfella
    • one year ago
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    its always worth checking to see if you can factor by grouping

  21. welshfella
    • one year ago
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    you cant always do it of course

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