Questions: Divide using synthetic division (3x^3-2x^2+5x-1)-(x-2)

Transcript text: Divide using synthetic division \[ \left(3 x^{3}-2 x^{2}+5 x-1\right)-(x-2) \]

Solution

Solution Steps

Step 1: Set Up

Given polynomial: $P(x) = 3x^3 - 2x^2 + 5x - 1$ Divisor: $x - (-2)$

Step 2: Perform Synthetic Division

The synthetic division process is carried out as follows: Divisor constant: 2 Bring down the leading coefficient: 3 Add and multiply: -2 + (-2) * 3 = -8 Add and multiply: 5 + (-2) * -8 = 21 Add and multiply: -1 + (-2) * 21 = -43

Step 3: Result Interpretation

The quotient polynomial is: $Q(x) = 3x^2 - 8x + 21$ The remainder is: -43

Final Answer:

The result of dividing the given polynomial by the binomial divisor is $Q(x) = 3x^2 - 8x + 21$ with a remainder of -43.

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