Refresh my memory. For the following polynomial, HOW would I find the X-int, the Factors, and the Roots? I know how to do this with quadratics, but I forgot how to do this with degrees larger than 2...

Question

anonymous · Answer

$\ \huge 4x^5+8x^4-5x^3+8x^2+28x-16 $.

alexwee123 · Answer

try rational root theorem  to find the factors :/

anonymous · Answer

?

alexwee123 · Answer

here look at this site http://hanlonmath.com/pdfFiles/30.RationalRootTheorem.pdf i'm too lazy to explain :/

anonymous · Answer

That doesnt make much sense... Could someone explain it to me?

alexwee123 · Answer

ok here is an example
2x² + 5x – 12 = 0
The factors of the leading coefficient 2 are ± 1,2
the factors of the constant -12 are ±1,2,3,4,6,12
now the rational root theorem states that all possible roots of a polynomial can be found through from factors of constant over factors of the leading coefficient  
for this example the possible rational roots are ±12 /2, 12/ 1, 6 /2, 6/ 1, 4/ 2, 4/ 1, 3/ 2, 3 /1, 2/ 2, 2/ 1, 1/ 2, and 1/ 1

alexwee123 · Answer

then you would try factoring out the polynomial with one of the possible roots through synthetic division or some other way until you find a valid solution

alexwee123 · Answer

also some of the roots can repeat