shresthakritagya59
Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

It is given that 2x³-7x²+x+10 = (x - 1) Q(j) + R. Find the remainder R and polynomial Q(j).​

Sagot :

mhanifa

Answer:

  • 2x²- 5x - 4, remainder 6

Step-by-step explanation:

Divide the given by x - 1:

x - 1 | 2x³ - 7x² + x + 10 = 2x²- 5x - 4  rem 6

       | 2x³ - 2x²

               -5x² + x

              -5x² + 5x

                        - 4x + 10

                        - 4x + 4

                                  6

2x³-7x²+x+10 = (x - 1)(2x²- 5x - 4) + 6

semsee45

Answer:

[tex]\large \text{$ Q(j) = 2x^2 - 5x - 4 $}[/tex]

[tex]\large \text{R = 6}[/tex]

Step-by-step explanation:

Use long division to find the polynomial and remainder:

[tex]\large \begin{array}{r}2x^2-5x-4\phantom{)}\\x-1{\overline{\smash{\big)}\,2x^3-7x^2+x+10\phantom{)}}}\\\underline{-~\phantom{(}(2x^3-2x^2)\phantom{-b)))))))}}\\0-5x^2+x+10\phantom{)}\\\underline{-~\phantom{()}(-5x^2+5x)\phantom{-b))}}\\0-4x+10\phantom{)}\\\underline{-~\phantom{()}(-4x+\phantom{)}4)}\\6\phantom{)}\end{array}[/tex]

Therefore:

[tex]\large \text{$2x^3 - 7x^2 + x + 10 = (x - 1)(2x^2 - 5x - 4) + 6$}[/tex]

So the polynomial and remainder are:

  • [tex]\large \text{$ Q(j) = 2x^2 - 5x - 4 $}[/tex]
  • [tex]\large \text{R = 6}[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.