Question 199258: Could someone explain how I should solve these three problems;
Use the synthetic substitution to find the value of f(-2) for f(x)=x^3-3x^2-x-9.
Use the Factor Theorem to determine whether (x-3) is a factor of f(x)=x^4+12x^3+6x+27.
In x^3-4x^2+2x+1=0, how many possible positive and how many possible negative roots are there?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the synthetic substitution to find the value of f(-2) for f(x)=x^3-3x^2-x-9.
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-2)....1....-3....-1....-9
.........1....-5....9...|..-27
f(-2) = -27
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Use the Factor Theorem to determine whether (x-3) is a factor of f(x)=x^4+12x^3+6x+27.
3)....1....12....0....6....27
........1....15...45...141..|..450
Since f(3) is not zero, x-3 is not a factor.
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In x^3-4x^2+2x+1=0, how many possible positive and how many possible negative roots are there?
In f(x) there are 2 changes of sign, so 0 or 2 positive roots.
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f(-x) = -x^3 - 4x^2 - 2x + 1
In f(-x) there are 2 changes of sign, so there are 0 or 2 negative roots.
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Cheers,
Stan H.
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