Explanation Given: 28 x 2 − 29 x + 6 4 x − 3 Key concept applied: Step 1: Set up the long division. The divisor (what we are dividing by) goes on the outside of the box. The dividend (what we are dividing into) goes on the inside of the box. When you write out the dividend and divisor, make sure that you insert 0's for any missing terms. Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. Step 3: Take the term found in step 1 and multiply it times the divisor. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. Step 4: Subtract this from the line above. Make sure that you subtract EVERY term found in step 3, not just the first one. Step 5: Repeat the process from step 1 to step 4 until done. That is till the degree of the subtracted term is less than the degree of the divisor. Step 6: Write out the answer. Your answer is the quotient that you ended up with on the top of the division box. If you have a remainder, write it over the divisor in your final answer. That is in the below format: D i v i d e n d D i v i s o r = Q u o t i e n t + Re m a i n d e r D i v i s o r (Or) D i v i d e n d = ( Q u o t i e n t ) ( D i v i s o r ) + Re m a i n d e r Formula used: D I V i d e n d = ( Q u o t i e n t ) ( D i v i s o r ) + Re m a i n d e r Calculation: Description 28 x 2 − 29 x + 6 4 x − 3 Step 1: Set up the long division. The divisor (what we are dividing by) goes on the outside of the box. The dividend (what we are dividing into) goes on the inside of the box. When you write out the dividend and divisor, make sure that you insert 0's for any missing terms 28 x 2 − 29 x + 6 4 x − 3 Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Take the quotient and multiply it times the divisor. 28 x 2 4 x = 7 x 7 x ( 4 x − 3 ) = 28 x 2 − 21 x Step 3: Write the result of multiplying quotient with divisor and place it under dividend. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. 7 x 4 x − 3 28 x 2 − 29 x + 6 28 x 2 − 21 x Step 4: Subtract this from the line above. Make sure that you subtract EVERY term found in step 3, not just the first one. 7 x 4 x − 3 28 x 2 − 29 x + 6 28 x 2 − 21 x ( − ) ( + ) _ − 8 x + 6 Step 5: Repeat the process from step 2 to step 4 until done. That is till the degree of the subtracted term is less than the degree of the divisor Step 2: Divide 1st term of divisor by first term of dividend to get first term of the quotient. The quotient (answer) is written above the division box. Take the quotient and multiply it times the divisor. − 8 x 4 x = − 2 − 2 ( 4 x − 3 ) = − 8 x + 6 Step 3: Write the result of multiplying quotient with divisor and place it under dividend. Make sure that you line up all terms of this step with the term of the dividend that has the same degree. 7 x − 2 4 x − 3 28 x 2 − 29 x + 6 28 x 2 − 21 x ( − ) ( + ) _ − 8 x + 6 − 8 x + 6 Calculation Continued: Repeating Step 4: Subtract this from the line above

5th Edition

ISBN: 9781260147117

Author: Miller

Publisher: MCG

See similar textbooks

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 4.4, Problem 32PE

To determine

Identity the divisor, quotient, and remainder of given long division and check by multiplication

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.4, Problem 31PE

Chapter 4.4, Problem 33PE

Students have asked these similar questions

On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by- hour, had failed - what if the Bergen public would find out? How would they plan their weekend without up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room. Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could they fake the data? At least for some hours (until the measurements would work again)? He used to spend a lot of time online and thus knew the value of fake data, especially when it spread fast! He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love yourself!" - back then, they had installed top-modern technology that not only measured the air temperature itself, but also its 1st, 2nd, 3rd, 4th, and…

Consider a forest where the population of a particular plant species grows exponentially. In a real-world scenario, we often deal with systems where the analytical function describing the phenomenon is not available. In such cases, numerical methods come in handy. For the sake of this task, however, you are provided with an analytical function so that you can compare the results of the numerical methods to some ground truth. The population P(t) of the plants at time t (in years) is given by the equation: P(t) = 200 0.03 t You are tasked with estimating the rate of change of the plant population at t = 5 years using numerical differentiation methods. First, compute the value of P'(t) at t = 5 analytically. Then, estimate P'(t) at t = 5 years using the following numerical differentiation methods: ⚫ forward difference method (2nd-order accurate) 3 ⚫ backward difference method (2nd-order accurate) ⚫ central difference method (2nd-order accurate) Use h = 0.5 as the step size and round all…

Nicole organized a new corporation. The corporation began business on April 1 of year 1. She made the following expenditures associated with getting the corporation started: Expense Date Amount Attorney fees for articles of incorporation February 10 $ 40,500 March 1-March 30 wages March 30 6,550 March 1-March 30 rent Stock issuance costs March 30 2,850 April 1-May 30 wages Note: Leave no answer blank. Enter zero if applicable. April 1 May 30 24,000 16,375 c. What amount can the corporation deduct as amortization expense for the organizational expenditures and for the start-up costs for year 1 [not including the amount determined in part (b)]? Note: Round intermediate calculations to 2 decimal places and final answer to the nearest whole dollar amount. Start-up costs amortized Organizational expenditures amortized

Chapter 4 Solutions

INTERMEDIATE ALGEBRA (LL)-W/ACCESS

Ch. 4.1 - a. A(n)_____________ is used to show repeated...Ch. 4.1 - Prob. 2PE Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 4PE Ch. 4.1 - For exercises 4-9, write an example of each...Ch. 4.1 - Prob. 6PE Ch. 4.1 - Prob. 7PE Ch. 4.1 - Prob. 8PE Ch. 4.1 - Prob. 9PE Ch. 4.1 - Prob. 10PE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.