SOLUTION: write as a product of linear factors and list all zeros: f(x)= 12^4 + 7x^3 - 22x^2

SOLUTION: write as a product of linear factors and list all zeros: f(x)= 12^4 + 7x^3 - 22x^2 - 7x +10

Question 160914: write as a product of linear factors and list all zeros:
f(x)= 12^4 + 7x^3 - 22x^2 - 7x +10
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
write as a product of linear factors and list all zeros:
f(x)= 12^4 + 7x^3 - 22x^2 - 7x +10
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Since the coefficients add up to zero, x=1 is a root of f(x)
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Use synthetic division:
1)....12....7....-22....-7....10
........12...19....-3....-10..|..0
-1).......12....7....-10..|..0
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So, you have roots at x= 1 and x=-1
You are left with a quadratic which you can solve in several ways:
x = [-7 +- sqrt(49 - 4*12*-10)]/24
x = [-7 +- sqrt(529)]/24
x = [-7 +- 23]/24
z = 16/24 or z = -30/24
z = 2.3 or z = -5/4
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Cheers,
Stan H.
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