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What are the factors of the polynomial function?

Use the rational root theorem to determine the factors.

f(x)=2x^3+x^2−8x−4                   

 Nov 1, 2018

Best Answer 

 #1
avatar+6252 
+2

The possible rational roots are of the form pqwhere p is a factor of the constant term, in this case -4and q is a factor of the highest order term, i.e. 2so possible roots arefactors of -4 are±1, ±2, ±4factors of 2 are ±1, ±2so our possible roots arex=±12, ±1, ±2, ±4

 

we plug these into f(x) to determine which are actually rootsand see that x=2, 12, 2are the only actual roots, and as f(x) is degree 3 that is all 3 of themso f(x)=c(x+2)(x+12)(x2), for some cQc is the coefficient of the x3 term sof(x)=2(x+2)(x+12)(x2)

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 Nov 1, 2018
edited by Rom  Nov 2, 2018
 #1
avatar+6252 
+2
Best Answer

The possible rational roots are of the form pqwhere p is a factor of the constant term, in this case -4and q is a factor of the highest order term, i.e. 2so possible roots arefactors of -4 are±1, ±2, ±4factors of 2 are ±1, ±2so our possible roots arex=±12, ±1, ±2, ±4

 

we plug these into f(x) to determine which are actually rootsand see that x=2, 12, 2are the only actual roots, and as f(x) is degree 3 that is all 3 of themso f(x)=c(x+2)(x+12)(x2), for some cQc is the coefficient of the x3 term sof(x)=2(x+2)(x+12)(x2)

Rom Nov 1, 2018
edited by Rom  Nov 2, 2018
 #2
avatar+234 
+1

thank you

skye25  Nov 1, 2018

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