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lidiya
2 months ago
11

Add one term to the polynomial expression 14x^19 - 9x^15 + 11x^4 + 5x^2 + 3 to make it into a 22nd degree polynomial

Mathematics
1 answer:
zzz [12.3K]2 months ago
7 0

Given:

The polynomial is

14x^{19}-9x^{15}+11x^4+5x^2+3

To find:

A term to add to the given polynomial to transform it into a 22nd degree polynomial.

Solution:

The degree of a polynomial corresponds to the highest exponent of its variable.

In this case, the highest power of x is 19, indicating the polynomial’s degree is 19.

To elevate it to a 22nd degree polynomial, we must introduce a term with a power of x equal to 22.P(x)=14x^{19}-9x^{15}+11x^4+5x^2+3

We can append

, where k is a constant.

Thus, we will add

to the initial polynomial.

kx^{22}

x^{22}After this addition, the polynomial's degree will be 22.

P(x)=x^22+14x^{19}-9x^{15}+11x^4+5x^2+3Therefore, the necessary term is

.

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