Jespraisicia 3 years ago Factor completely: 2x3 + 10x2 + 4x + 20

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1. mathslover

first of all find the factors of +20 do you know the factors of 20?

2. Callisto

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

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

@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

okay .. sorry !

6. mathslover

@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

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

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

ok wait lemme show my full work

10. Callisto

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

this is what i did

12. mathslover

Very right @Callisto It is factor theorem .. but yes it takes a long time

13. mathslover

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

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

right