Question

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

Answer 1

Given:

The polynomial is

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

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,

$P(x)=14x^{19}-9x^{15}+11x^4+5x^2+3$

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 $kx^{22}$, where k is constant.

So add $x^{22}$ in the given polynomial.

$P(x)=x^22+14x^{19}-9x^{15}+11x^4+5x^2+3$

Now, the degree of polynomial is 22.

Therefore, the required term is $x^{22}$.