The polynomial 2x 4 + 3x 3 12x 2 7x + a is denoted by

Question:

The polynomial 2x⁴ + 3x³ − 12x² − 7x + a is denoted by p(x).
a. Given that (2x − 1) is a factor of p(x), find the value of a.
b. When a has this value, verify that (x + 3) is also a factor of p(x) and hence factorise p(x) completely.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Mar 09, 2023 06:50 AM

See More Questions

Factor A Factor B 1 2 3 4 Xj for Factor B 1 2 3 4 1 2500 2 9 10 6 9 8500 3 14 11 16 12 13250 Xi for Factor A 8333 8000 9000 7333 X8083
Verify that U1 and U2 are also given by And i(n1)
Verify that the 1-year forward rate 3 years hence in Figure 25.5 is 14.0134%. In Figure 25.5 Year 0 Ye Year 2 Year 3 20.03% 20.1 7% 13.22% 15.68% 10% 13.66% 10.82% 12.28% 9.25% 9.62%
Name the types of consumer decision-making processes. List some products you have bought using each type. Have you ever bought a product on impulse? If so, describe the circumstances.
According to JiWire, Inc., the top 10 countries by number of Wi-Fi locations, as of October 27, 2008, are as shown in the following table. Identify the type of data provided by the information in...
Imagine you own a small business and after a year in business you have decided to hire a bookkeeper for 2 hours every Friday to bring your books up to date and to process payroll. You want the work...
As the marketing manager for Independent Packaging Pty Ltd, you have asked the accountant what it costs to make the Container2000 model because you want to set a price for the container. A similar...
Information related to Gustavo Company for 2012 is summarized below. Total credit sales $1,100,000 Accounts receivable at December 31 369,000 Bad debts written off 22,150 Instructions (a) What amount...
Zoe Corporation has the following information for the month of March: Cost of direct materials used in production $18,132 Direct labor 24,624 Factory overhead 35,790 Work in process inventory, March...
The maintenance staff of a large office building regularly replaces fluorescent ceiling lights that have gone out. During a visit to a typical floor, the staff may have to replace several lights. The...
Find the set of values for k for which the equation 3x 4 + 4x 3 12x 2 + k = 0 has four real roots.
You are given that the equation x 3 + ax 2 + bx + c = 0 has three real roots and that these roots are consecutive terms in an arithmetic progression. Show that 2a 3 + 27c = 9ab.
Greenwich Industries has forecasted its monthly needs for working capital (net of spontaneous sources, such as accounts payable) for 2013 as follows: Short-term borrowing (that is, a bank line of...
You are considering an investment that is going to pay $1,500 a month starting 20 years from today for 15 years. If you can earn an 8 percent return on any investment, compounded monthly, how much at...
Discuss in a short paragraph (3-5+ sentences) how the theory of the diffusion of innovation does or does not apply to your communication campaign.
Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a)...
For the second half of the semester, you will be working in the role of student intern at the Conestoga Consulting Company, does a lot of consulting for Conestoga College and companies near the...
Draw the Lewis structures of two possible arrangements of atoms of hypofluorous acid-HOF and HFO.
Same as Problem 24.34, except use a 300-ft spiral for the curve of Problem 24.8.
The water in tank A is at 270 F with quality of 10% and mass 1 lbm. It is connected to a piston/cylinder holding constant pressure of 40 psia initially with 1 lbm water at 700 F. The valve is opened,...
A small company sells glass, which it cuts to size to fit into window frames. How could the company benefit from knowing the modal size of glass its customers purchase?
Speeds, measured in metres per second, are denoted by x. Find the constant k such that kx denotes the speeds in kilometres per hour.
The lengths of 2500 bolts, xmm, are summarised by (x 40) = 875. Find the mean length of the bolts.
QUESTION 13.3 (Rentalproperty,capitalallowances) Alf Ericsson, a resident Australian taxpayer, owns a house in Sydney from which he derives rental income. During the tax year, Alf had the following...
Keeper Ltd. has 50,000 no par value common shares authorized, issued, and outstanding. All 50,000 shares were issued at $4 per share. Retained earnings are $60,000. If 5,000 common shares were...
A monthly depositor has accumulated $110,000 in fica and federal income taxes in their payable account as of July. 31. Which of the follow would be correct? Group of answer choices No deposit is...

The polynomial 2x 4 + 3x 3 12x 2 7x + a is denoted by

Question:

Step by Step Answer:

a If 2x 1 is a factor of px then we know that there exists some polynomial q...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions