Answer:
[tex]-x^2+2x-3[/tex]
Step-by-step explanation:
We have [tex](x^2- 3x) + (-2x^2 + 5x -3)[/tex] which is the same as:
[tex]x^2-3x-2x^2+5x-3[/tex]
The polynomial has 5 terms that we are going to analyse:
1st. term: [tex]x^2[/tex] Degree: 2 Coefficient: 1
Observation: Coefficient is the number in front of a variable. In this case the variable is x. Then the first term has coefficient 1 because [tex](1).x^2=x^2[/tex].
2nd. term: [tex]-3x[/tex] Degree:1 Coefficient: (-3)
3rd. term: [tex]-2x^2[/tex] Degree:2 Coefficient: (-2)
4th. term: [tex]5x [/tex] Degree:1 Coefficient: 5
5th. term: [tex]-3[/tex] Degree:0 Coefficient: (-3)
We have to reorder the polynomial writing each term in order of degree from highest to lowest (left to right).
The terms with highest degree are the first and third. Then the second and fourth term. And the lowest degree corresponds to the fifth term.
The polynomial now is:
[tex]x^2-2x^2-3x+5x-3[/tex]
Now we have to sum the terms that have the same degree:
[tex]x^2-2x^2=(1-2)x^2=(-1)x^2=-x^2[/tex]
[tex]-3x+5x=(-3+5)x=2x[/tex]
Then the result is:
[tex]-x^2+2x-3[/tex]
