SOLUTION: I am having trouble with this homework problem, I'm not sure what to do could you please help me:
Use the polynomial that defines P as the dividend and the binomial that defines D
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-> SOLUTION: I am having trouble with this homework problem, I'm not sure what to do could you please help me:
Use the polynomial that defines P as the dividend and the binomial that defines D
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Question 443086: I am having trouble with this homework problem, I'm not sure what to do could you please help me:
Use the polynomial that defines P as the dividend and the binomial that defines D as the divisor. Write the division in the form P(x)=D(x) x Q(x)+R where the polynomial that defines Q is the quotient and R is an integar remainder for the equation P(x)=2x^3-5x^2+8x-5; D(x)= x - 1 Found 2 solutions by stanbon, swincher4391:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I am having trouble with this homework problem, I'm not sure what to do could you please help me:
Use the polynomial that defines P as the dividend and the binomial that defines D as the divisor. Write the division in the form P(x)=D(x) x Q(x)+R where the polynomial that defines Q is the quotient and R is an integar remainder for the equation P(x)=2x^3-5x^2+8x-5; D(x)= x - 1
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Divide P(x) by D(x) to find Q(x) and R
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Using synthetic division I get:
1)....2....-5....8....-5
.......2.....-3...5...|..0
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Q(x) = Quotient = 2x^2-3x+5
R = Remainder = 0
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P(x) = (x-1)(2x^2-3x+5)+0
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Cheers,
Stan H.
You can put this solution on YOUR website! This is just a fancy way of them saying: DO LONG DIVISION. Then take your solution and multiply it by your dividend to get your original polynomial. So let's do it:
x-1 | 2x^3 -5x^2 + 8x -5
How many times does x go into 2x^3? 2x^2 times.
(x-1)*2x^2 = 2x^3 +2x^2
2x^3 -5x^2 + 8x -5
-(2x^3 -2x^2 +0 + 0)
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0 -3x^2 + 8x - 5
How many times does x go into -3x^2? -3x times.
(x-1)*(-3x) = -3x^2 + 3x
-3x^2 +8x 0 -5
-(-3x^2 + 3x +0)
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0 +5x - 5
How many times does x go into 5x? 5 times.
(x-1)*5 = 5x -5
5x-5
-(5x-5)
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0
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So we have our Q(x) + R =
So then,
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Let's check this
Check.
So then our representation is correct.
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