/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Use long division to divide. $... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 11

Use long division to divide. $$\left(2 x^{2}+10 x+12\right) \div(x+3)$$

Short Answer

Expert verified
The quotient resulting from the division is \(2x + 4\).

Step by step solution

01

Set up the Long Division

First, the long division needs to be set up correctly. It is important to ensure that the polynomial \(2x^{2} + 10x + 12\) is in the right order. The divisor (x+3) is also in the correct form. Hence, the setup for the long division is as follows: with \(2x^2+10x+12\) inside and \(x+3\) outside the division symbol.
02

Dividing and Subtracting

Begin by dividing the first term of the divisor \(x\) into the first term of the dividend \(2x^2\). This results in \(2x\). Now multiply the divisor by \(2x\) and subtract this from the dividend. This gives the equation: \(2x^2+10x+12-((x+3)2x)= 4x+12\).
03

Repeating the Process

Repeat the division, this time using the new dividend \(4x+12\). Divide the first term of the divisor \(x\) into the first term of the dividend \(4x\). This results in \(4\). Multiplying the divisor by \(4\) gives \(4x+12\), and doing the subtraction yields 0. This indicates that the division process is complete.
04

Writing the Final Answer

The solution to the division should be the expressions obtained that is the quotient. The solution is given by adding the terms obtained from each division, hence the quotient is given by the equation \(2x + 4\).

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Most popular questions from this chapter

Geometry You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides. (a) Let \(x\) represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box. (b) Use the diagram to write the volume \(V\) of the box as a function of \(x .\) Determine the domain of the function. (c) Sketch the graph of the function and approximate the dimensions of the box that will yield a maximum volume. (d) Find values of \(x\) such that \(V=56 .\) Which of these values is a physical impossibility in the construction of the box? Explain.

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