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Chapter 2: Problem 12

Use long division to divide. \(\left(5 x^{2}-17 x-12\right) \div(x-4)\)

Short Answer

Expert verified
The result of the division \(\left(5 x^{2}-17 x-12\right) \div(x-4)\) is \(5x +3\).

Step by step solution

01

Set up the Long Division

Firstly, set the division up like this: \(\frac{5x^2 -17x -12}{x - 4}\). Here, \(5x^2 -17x -12\) is the dividend and \(x -4\) is the divisor.
02

Divide the First Term

Next, divide the first term of the dividend, \(5x^2\), by the first term of the divisor, \(x\). This results in \(5x\) which would be the first term of quotient.
03

Multiply and Subtract

Multiply back \(5x\) with the divisor \(x - 4\), which results in \(5x^2 -20x\). Subtract this from the originally dividend, we get \(\left( 5x^2 -17x -12\right) - \left( 5x^2 - 20x \right)\), this simplifies to \(3x -12\).
04

Repeat the Process

Divide the first term of the new dividend (which is \(3x\)) by the first term of the divisor (which is \(x\)). This results in \(3\) which will be the next term of our quotient. Next, multiplying back \(3\) with the divisor \(x - 4\), which gives \(3x-12\), subtract this from the previous remainder \(3x - 12\), this gives us \(0\). Now, we have no remainder left and thus have finished the division.

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