Question 193519: USE Rational Zeros Theorem to create a list of possible rational zeros for :
x^3+2x^2-13x+10
Using list from above and synethetic division determine the zeros of x^3+2x2-13x+10
Write P(x) = x^3+2x^2-13x+10 as a product.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! x^3+2x^2-13x+10
factor is 1st or last terms might be ,,,(p/q),,,,+/-(1/1,10/1,2/1,5/1)
using synthetic division (pls ignore commas,, used for spacing)
1| 1,,,,,,+2,,,,,,-13,,,,,,10
,,,,,,,,,,,,,,,1,,,,,,,,,,,3,,,,,-10
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,,,,,,1,,,,,,,3,,,,,,,,-10,,,,,,0,,,,,,,,(no remainder,therefore x=1 is zero,(x-1) is factor)
quotient is 1x^2+3x-10
factoring,,,(x+5)(x-2)
therefore total factors are
(x-1)(x+5)(x-2)
check by distributing
(x+5) (x-2)(x-1)
(x+5) (x^2-3x+2)
x^3-3x^2+2x+5x^2-15x+10
x^3 +2x^2-13x +10 ,,,,ok
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