Questions: Select the correct equation represented by the synthetic division problem. 3 1 1 -14 6 3 12 -6 1 4 -2 (x^3+x^2-14x+6) ÷ (x+3) = x^2+4x-2 (x^3+x^2-14x+6) ÷ (x-3) = x^2+4x-2 (-x^3-x^2+14x-6) ÷ (x-8) = x^2-4x+2

Select the correct equation represented by the synthetic division problem. 3 1 1 -14 6 3 12 -6 1 4 -2 (x^3+x^2-14x+6) ÷ (x+3) = x^2+4x-2 (x^3+x^2-14x+6) ÷ (x-3) = x^2+4x-2 (-x^3-x^2+14x-6) ÷ (x-8) = x^2-4x+2
Transcript text: 3. Select the correct equation represented by the synthetic division problem. \[ \left.3 \begin{array}{rrrr} 1 & 1 & -14 & 6 \\ & 3 & 12 & -6 \\ \hline & 1 & 4 & -2 \end{array}\right) \] $\left(x^{3}+x^{2}-14 x+6\right) \div(x+3)=x^{2}+4 x-2$ $\left(x^{3}+x^{2}-14 x+6\right) \div(x-3)=x^{2}+4 x-2$ $\left(-x^{3}-x^{2}+14 x-6\right) \div(x-8)=x^{2}-4 x+2$
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Solution

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Solution Steps

Step 1: Identify the divisor in the synthetic division

The synthetic division problem is set up with the divisor \( x + 3 \). This is because the number used in the synthetic division is \(-3\) (the root of \( x + 3 = 0 \)).

Step 2: Verify the dividend and quotient

The dividend in the synthetic division is \( x^{3} + x^{2} - 14x + 6 \). The quotient obtained from the synthetic division is \( x^{2} + 4x - 2 \).

Step 3: Match the correct equation

The correct equation represented by the synthetic division is: \[ \left(x^{3} + x^{2} - 14x + 6\right) \div (x + 3) = x^{2} + 4x - 2 \] This matches the first option provided.

Final Answer

The correct answer is A.

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