calebbarnes76
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Given the polynomial 21x 4 + 3y - 6x 2 + 34

What polynomial must be subtracted from it to obtain 29x 2 - 7 ?
What polynomial must be added to it to obtain a first degree polynomial?

Answer :

34-6x^2, 21x^4/3y  4 is the degree of the polynomail
frika

Consider the polynomial [tex]21x^4 + 3y - 6x^2 + 34.[/tex] This polynomial has four terms:

  • term [tex]21x^4[/tex] of 4th degree;
  • term [tex]3y[/tex]  of 1st degree;
  • term [tex]-6x^2[/tex] of 2nd degree;
  • term [tex]34[/tex] of 0 degree or simply the coefficient without variables.

1. What polynomial must be subtracted from it to obtain [tex] 29x^2 - 7?[/tex]

You must take off first and second terms at all and add termw with [tex]x^2[/tex] and coefficient. Thus, you have to subtract polynomial [tex]21x^4+3y-35x^2+41[/tex].

Check:

[tex]21x^4 + 3y - 6x^2 + 34-(21x^4+3y-35x^2+41)=21x^4+3y-6x^2+34-21x^4-3y+35x^2-41=x^2(-6+35)+(34-41)=29x^2-7.[/tex]

2. What polynomial must be added to it to obtain a first degree polynomial?

If you want to obtain a 1st degree polynomial, then you must take off terms of 4th and 2nd degree. So you have to add [tex]-21x^4+6x^2.[/tex]

Check:

[tex]21x^4 + 3y - 6x^2 + 34+(-21x^4+6x^2)=21x^4 + 3y - 6x^2 + 34-21x^4+6x^2=3y+34.[/tex]

Answer: 1) [tex]21x^4+3y-35x^2+41[/tex] 2) [tex]-21x^4+6x^2.[/tex]

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