The difference is [tex]7x^{2} + 1x-7[/tex].
Step-by-step explanation:
Step 1:
The polynomial [tex]-5x^{2}+3x+8[/tex] is subtracted from the polynomial [tex]2x^{2} + 4x +1[/tex].
If we write this as an equation, we get
[tex](2x^{2} + 4x +1) -(-5x^{2}+3x+8)[/tex].
To subtract the polynomials, we group up the terms based on their variables.
In this subtraction, there are two variables i.e. [tex]x^{2}[/tex] and [tex]x[/tex] and there is one constant term.
Step 2:
The subtraction of the [tex]x^{2}[/tex] variables; [tex]2x^{2} -(-5x^{2} ) = 2x^{2} +5x^{2} = 7x^{2}[/tex].
The subtraction of the [tex]x[/tex] variables; [tex]4x - (3x) = 1x[/tex].
The subtraction of the constants; [tex]1-(8) = -7[/tex].
So [tex](2x^{2} + 4x +1) -(-5x^{2}+3x+8) = 7x^{2} + 1x-7[/tex].
