Given:
The polynomial is
[tex]14x^{19}-9x^{15}+11x^4+5x^2+3[/tex]
To find:
One term which is used to add in given polynomial to make it into a 22nd degree polynomial.
Solution:
Degree of a polynomial is the highest power of the variable.
Let,
[tex]P(x)=14x^{19}-9x^{15}+11x^4+5x^2+3[/tex]
Here, the highest power of x is 19, so degree of polynomial is 19.
To make it into a 22nd degree polynomial, we need to need a term having 22 as power of x.
We can add [tex]kx^{22}[/tex], where k is constant.
So add [tex]x^{22}[/tex] in the given polynomial.
[tex]P(x)=x^22+14x^{19}-9x^{15}+11x^4+5x^2+3[/tex]
Now, the degree of polynomial is 22.
Therefore, the required term is [tex]x^{22}[/tex].
The required polynomial to a 22nd degree is [tex]P(x)=x^{22}+14x^{19} - 9x^{15} + 11x^4 + 5x^2[/tex]
Given the polynomial function, [tex]14x^{19} - 9x^{15} + 11x^4 + 5x^2[/tex],, we are to add one term to the polynomial to make it into a 22nd-degree polynomial.
Note the highest and leading power of the variable of any function is the degree of such function.
To convert the given polynomial to a 22nd-degree function, we will simply add a variable term x with a degree of 22 to have:
[tex]P(x)=x^{22}+14x^{19} - 9x^{15} + 11x^4 + 5x^2[/tex]
Hence the required polynomial to a 22nd degree is [tex]P(x)=x^{22}+14x^{19} - 9x^{15} + 11x^4 + 5x^2[/tex]
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