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Jespraisicia

  • 2 years ago

Factor completely: 2x3 + 10x2 + 4x + 20

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  1. mathslover
    • 2 years ago
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    first of all find the factors of +20 do you know the factors of 20?

  2. Callisto
    • 2 years ago
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    Take out the common factor of the first two terms and last two terms. 2x^3 + 10x2 + 4x + 20 = 2x^2 (x+5) + 4(x+5) = ...?

  3. ashna
    • 2 years ago
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    2x^3 + 10x^2 + 4x + 20 = 0 (2x+10)(x^2+2) = 0 2x = -10 ; x^2 = -2 x = -5 ; x = √ -2 x = -5 ; x = + or -√ 2

  4. Callisto
    • 2 years ago
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    @ashna It's factoring the expression, not solving equation. Moreover, please don't give direct answers to the question. You may refer to our Code of Conduct at httlp://www.opnstudy.com/code-of-conduct for more information. Thanks.

  5. ashna
    • 2 years ago
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    okay .. sorry !

  6. mathslover
    • 2 years ago
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    @Callisto it can be done in this way also : factors of 20 = \(\large{\pm 1,\pm 2,\pm 4,\pm 5,\pm 10, \pm20}\) now given p(x) = 2x3 + 10x2 + 4x + 20 p(-5)=-250+250-20+20=0 hence -5 is a zero of the polynomial p(x) that is (x+5) is a factor of p(x)

  7. mathslover
    • 2 years ago
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    M i right in this way also ? please dont consider this as direct answer... it is my confusion it may be wrong and also the answer is not yet declared

  8. Callisto
    • 2 years ago
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    I haven't learnt this way. It may work, but for this question, it's not necessary to use this way, I think. @mathslover

  9. mathslover
    • 2 years ago
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    ok wait lemme show my full work

  10. Callisto
    • 2 years ago
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    Well, I understand this method. Probably, you're doing by factor theorem. It works but it just takes a long time for this question as you have to test for many factors.

  11. mathslover
    • 2 years ago
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    this is what i did

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  12. mathslover
    • 2 years ago
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    Very right @Callisto It is factor theorem .. but yes it takes a long time

  13. mathslover
    • 2 years ago
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    thanks to god that it was 20 .. if it was some other large number like 4000993 then it was next to impossible to do by this

  14. Callisto
    • 2 years ago
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    For this type of problem,usually, I would see if it can be done by taking out factors/identities first. If not, then I have to use factor theorem.

  15. mathslover
    • 2 years ago
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    right

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