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Question 69411This question is from textbook Algebra & Trigonometry with Geometry
: Missed the following on Chapter quiz; please help studying for exam:
Find a polynomial with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.
The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3).
Let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1.
Thanks...
This question is from textbook Algebra & Trigonometry with Geometry
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find a polynomial with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.
f(x)= (x+1)(x-1)(x-3)
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The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3).
f(3) equals the remainder which is 2.
f(3) = 2
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Let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1.
You are told that x=1 is a root or zero of f(x).
Divide f(x) by x-1 to find the other factor:
1)....1....-8....17....-9
.......1.....-7....10..|..1
COMMENT: That last number should be zero. I think you copied some part
of your problem incorrectly.
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Cheers,
Stan H.
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