Questions: Divide the expression. (8 x^3+14 x^2-8 x-14)/(2 x^2-2)

Solution Steps

To divide the given polynomial expression, we can perform polynomial long division. We will divide the numerator \(8x^3 + 14x^2 - 8x - 14\) by the denominator \(2x^2 - 2\).

We start with the polynomial expression to be divided: \[ \frac{8x^3 + 14x^2 - 8x - 14}{2x^2 - 2} \]

We divide the numerator \(8x^3 + 14x^2 - 8x - 14\) by the denominator \(2x^2 - 2\).

1. The leading term of the numerator \(8x^3\) divided by the leading term of the denominator \(2x^2\) gives us \(4x\).
2. Multiply \(4x\) by the entire denominator: \[ 4x(2x^2 - 2) = 8x^3 - 8x \]
3. Subtract this from the original numerator: \[ (8x^3 + 14x^2 - 8x - 14) - (8x^3 - 8x) = 14x^2 - 14 \]

Now, we divide \(14x^2 - 14\) by \(2x^2 - 2\):

1. The leading term \(14x^2\) divided by \(2x^2\) gives us \(7\).
2. Multiply \(7\) by the entire denominator: \[ 7(2x^2 - 2) = 14x^2 - 14 \]
3. Subtract this from the previous result: \[ (14x^2 - 14) - (14x^2 - 14) = 0 \]

Final Answer