Respuesta :
Note: As you may have unintentionally missed to add the different answers, based on which we had to check who solved correctly between Tamara and Clyda's work.
But, I am actually solving the expression and you must note that whoever (between Tamara and Clyda's work) may have got the same answer or match the answer with mine, would be the one who solved correctly.
Answer:
We conclude that whoever (between Tamara and Clyda's work) may have got the answer as [tex]x^2+5x-2[/tex] after dividing [tex]2x^4\:+\:7x^3\:-\:18x^2\:+\:11x\:-\:2[/tex] by [tex]2x^2\:-\:3x\:+\:1[/tex] , would be the one who solved it correctly.
Step-by-step explanation:
Considering the expression
[tex]2x^4\:+\:7x^3\:-\:18x^2\:+\:11x\:-\:2[/tex]
Lets divide the expression by [tex]2x^2\:-\:3x\:+\:1[/tex]
Solution Steps:
[tex]\frac{2x^4+7x^3-18x^2+11x-2}{2x^2-3x+1}[/tex]
Factorizing
[tex]2x^4+7x^3-18x^2+11x-2:\quad \left(x-1\right)\left(2x-1\right)\left(x^2+5x-2\right)[/tex]
[tex]\frac{\left(x-1\right)\left(2x-1\right)\left(x^2+5x-2\right)}{2x^2-3x+1}[/tex]
Factorizing
[tex]2x^2-3x+1:\quad \left(2x-1\right)\left(x-1\right)[/tex]
[tex]\frac{\left(x-1\right)\left(2x-1\right)\left(x^2+5x-2\right)}{\left(2x-1\right)\left(x-1\right)}[/tex]
[tex]\mathrm{Cancel\:}\frac{\left(x-1\right)\left(2x-1\right)\left(x^2+5x-2\right)}{\left(2x-1\right)\left(x-1\right)}:\quad x^2+5x-2[/tex]
[tex]x^2+5x-2[/tex]
Thus,
[tex]\frac{2x^4+7x^3-18x^2+11x-2}{2x^2-3x+1}=x^2+5x-2[/tex]
Therefore, we conclude that whoever (between Tamara and Clyda's work) may have got the answer as [tex]x^2+5x-2[/tex] after dividing [tex]2x^4\:+\:7x^3\:-\:18x^2\:+\:11x\:-\:2[/tex] by [tex]2x^2\:-\:3x\:+\:1[/tex] , would be the one who solved it correctly.
Keywords: expression, division
Learn more about expression division from brainly.com/question/1575482
#learnwithBrainly
The correct answer after division we get [tex]x^2+5x-2[/tex]. Thus, any of the students, Tamara or Clyde, can be correct who has got the same quotient as solved here.
Given:
Tamara and Clyde got different answers when dividing [tex]2x^4+7x^3-18x^2+11x-2[/tex] by [tex]2x^2-3x+1[/tex].
As per given question, we have to find the value of [tex]\frac{2x^4+7x^3-18x^2+11x-2}{2x^2-3x+1}[/tex].
Finding the factors of the numerator and denominator:
[tex]\frac{(x-1)(2x-1)(x^2+5x-2)}{(2x-1)(x-1)}=x^2+5x-2[/tex]
Here, we get the quotient as [tex]x^2+5x-2[/tex].
Therefore, any of the students, Tamara or Clyde, can be correct who has got the same quotient after division as [tex]x^2+5x-2[/tex].
Learn more about division of polynomial here:
https://brainly.com/question/12520197
