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Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2

Which answer is correct?

Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2 Which answer-example-1
Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2 Which answer-example-1
Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2 Which answer-example-2
Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2 Which answer-example-3
Anjelica is using synthetic division to divide 2x^3−9x^2−21x+10 by x+2 Which answer-example-4

1 Answer

5 votes

Answer: Choice B

1st row = -2, 2, -9, -21, 10

2nd row = -4, 26, -10

3rd row = 2, -13, 5, 0

The commas aren't part of the table but they are useful to separate the values.

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Step-by-step explanation

The values in the top row to the right of the vertical bar represent the coefficients of 2x^3-9x^2-21x+10. Those coefficients are 2, -9, -21, 10

The -2 off to the very left in this same row is the result of solving x+2 = 0 for variable x. This is known as the test root.

Drop the first coefficient down to the bottom row. Multiply that with the test root to get -4. We write -4 in the 2nd row just under the -9.

Then add -9 and -4 to get -13 as shown in choice B. The process of "multiply, add, multiply, add, etc" is repeated until the table is filled out.

The last value in the bottom row is the remainder. A remainder of 0 means (x+2) is a factor of 2x^3-9x^2-21x+10

The other values in the bottom row are coefficients for the quotient. The quotient is 2x^2-13x+5

Therefore, 2x^3-9x^2-21x+10 = (x+2)(2x^2-13x+5)

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