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headge

  • 3 years ago

You are given that f(x) = x^3 - 19x + 30 1.) Calculate f(0) and f(3). Hence write down a factor of f(x). Thanks.

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  1. headge
    • 3 years ago
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    @amistre64 @Hero

  2. mukushla
    • 3 years ago
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    can u evaluate f(0) and f(3) ?

  3. headge
    • 3 years ago
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    What does evaluate mean?

  4. mukushla
    • 3 years ago
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    calculate-compute-

  5. headge
    • 3 years ago
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    Hmmm hang on. Do you mean put them into the f(X)= thing?

  6. Hero
    • 3 years ago
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    Evaluate means to do this: f(x) = x^3 - 19x + 30 f(0) = (0)^3 - 19(0) + 30 = ? f(3) = (3)^3 - 19(3) + 30 = ?

  7. headge
    • 3 years ago
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    Yes ok Ill have a go at that and tell you what I got thanks.

  8. headge
    • 3 years ago
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    Right for f(0) I got 30 and the next one 0

  9. Hero
    • 3 years ago
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    f(3) = 0 Are you sure?

  10. headge
    • 3 years ago
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    Ill do it again

  11. headge
    • 3 years ago
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    Did it again and got 0 again.

  12. Hero
    • 3 years ago
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    f(3) = (3)^3 - 19(3) + 30 = 27 - 57 + 30 = 30 + 27 - 57 = 57 - 57 = 0 OK

  13. headge
    • 3 years ago
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    Yes!! So now I have two more questions. Are you up for helping?

  14. headge
    • 3 years ago
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    Wait what is the 'hence write down the factor of f(x)' bit?

  15. headge
    • 3 years ago
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    @nincompoop

  16. headge
    • 3 years ago
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    @estudier

  17. Hero
    • 3 years ago
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    If you calculated f(3) = 0, then (x-3) is a factor

  18. headge
    • 3 years ago
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    :) I remeber that now. The 0 ones it is.

  19. headge
    • 3 years ago
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    (ii) Find p and q such that f(x) = (x-2)(x^2 + px +q). How does one go about this?

  20. headge
    • 3 years ago
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    @karatechopper @myininaya

  21. headge
    • 3 years ago
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    @Coolsector

  22. Coolsector
    • 3 years ago
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    (x-2)(x^2 + px +q) = x^3 +px^2 +qx -2x^2 -2px -2q = x^3 +(p-2)x^2 +(q-2p)x - 2q and the orig is x^3 - 19x + 30 so we know that p-2 should be 0 and q-2p should be -19 and -2q should be 30 can you answer now ?

  23. headge
    • 3 years ago
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    Wait....Where has that big line came from? ohhh you timesed out the brackets! Ok wait a min.

  24. headge
    • 3 years ago
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    I get it up to when you start saying the so we know p-2=0 bit. I dont know how we know that.

  25. Coolsector
    • 3 years ago
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    ok you see we have a term (p-2)x^2 but in the general equation we dont have x^2 at all .. so we have to make it disappear .. we do this by saying p-2 = 0

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