Complete the synthetic division problem below.−3∣12−23‾−3 ∣12−23 What is the quotient in polynomial form?A.x2 + x - 3B.x2 + x - 1C.x2 - x + 3D.x2 - x + 1
Question
Complete the synthetic division problem below.
−3 | 12 -2 3
What is the quotient in polynomial form?
A. x² + x - 3
B. x² + x - 1
C. x² - x + 3
D. x² - x + 1
Solution
The synthetic division problem is not fully stated. However, I will show you how to solve a synthetic division problem using an example.
Let's say we have the problem -3 | 12 -23 -3. Here's how you would solve it:
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Write down the coefficients of the polynomial (12, -23, -3) in a row. Draw a line under them.
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Write the number you're dividing by (-3) to the left of the line.
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Bring down the first coefficient (12) below the line.
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Multiply the number you brought down (12) by the number you're dividing by (-3) and write the result (-36) under the second coefficient (-23).
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Add the numbers in this column (-23 + -36 = -59) and write the result below the line.
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Repeat steps 4 and 5 with the new number you brought down (-59) and the next coefficient (-3). Multiply -59 by -3 to get 177, write this under -3, and add to get 174.
So, the numbers below the line are the coefficients of the quotient polynomial. In this case, the quotient is 12x - 59 with a remainder of 174.
Please provide the complete synthetic division problem for a more accurate answer.
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