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Question 1034829: Can you help me with a synthetic division problem?
Which answer choice shows the correct setup in the following problem, by dividing using synthetic division?
Link to problem: http://postimg.org/image/hembcuok1/
thanks in advance..
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the synthetic division shows as:
-2 | 3 5 0 1 0 5
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the -2 comes from the divisor of x+2.
you take the divisor of x+2 and set it equal to 0 and then solve for x.
start with x+2 = 0.
subtract 2 from both sides of the equation to get x = -2
the divisor in the synthetic division is -2.
if you look at the dividend, the rightmost number is the constant and the expression goes up 1 degree at a time from there.
therefore, you get:
x^5 x^4 x^3 x^2 x c
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-2 | 3 5 0 1 0 5
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the dividend in the synthetic division is composed of the coefficients of the original equation.
each position in the dividend of the synthetic division is the coefficient of the corresponding variable in the original equation.
therefore, the original equation is:
3x^5 + 5x^4 + 0x^3 + x^2 + 0x + 5.
when the coefficient is 0, that particular variable disappears.
this makes your original equation 3x^5 + 5x^4 + x^2 + 5.
your original equation is being divided by x + 2.
when you do synthetic division, you have to insert the missing degrees going down from the highest degree term down to the lowest degree term.
the original equation is 3x^5 + 5x^4 + x^2 + 5.
the missing degrees are x^3 and x.
you insert them with a 0 coefficient.
you then get:
3x^5 + 5x^4 + 0x^3 + x^2 + 0x + 5.
to perform the synthetic division, you just take the coefficients in descending order of degree to get 3 5 0 1 0 5.
the divisor is x+2.
to find the divisor of the synthetic division, you set x+2 = 0 and solve for x to get x = -2.
the divisor in the synthetic divisor is -2.
your original equation is 3x^5 + 5x^4 + x^2 + 5 and it is being divided by x+2.
that looks like selection B in your picture.
a tutorial on synthetic division can be found here.
http://www.purplemath.com/modules/synthdiv.htm
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