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Jespraisicia
 2 years ago
Factor completely: 2x3 + 10x2 + 4x + 20
Jespraisicia
 2 years ago
Factor completely: 2x3 + 10x2 + 4x + 20

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mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0first of all find the factors of +20 do you know the factors of 20?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Take 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) = ...?

ashna
 2 years ago
Best ResponseYou've already chosen the best response.12x^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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1@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/codeofconduct for more information. Thanks.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0@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+25020+20=0 hence 5 is a zero of the polynomial p(x) that is (x+5) is a factor of p(x)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0M 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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1I haven't learnt this way. It may work, but for this question, it's not necessary to use this way, I think. @mathslover

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0ok wait lemme show my full work

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Well, 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.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Very right @Callisto It is factor theorem .. but yes it takes a long time

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0thanks 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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1For 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.
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