Answer:
The new expression is [tex]p' = 5\cdot x^{2}+11\cdot x^{4}-9\cdot x^{15}+14\cdot x^{19}+12\cdot x^{22}[/tex].
Step-by-step explanation:
A polynomial is a sum of algebraic monomials such that:
[tex]p = \Sigma_{i=0}^{n} c_{i}\cdot x^{i}[/tex]
Where [tex]n[/tex] is the degree of the polynomial and [tex]c_{i}[/tex] is the i-th coefficient of the polynomial. A 22nd degree polynomial has [tex]n = 22[/tex], so that given polynomial must added by a monomial with grade 22. Thus:
If [tex]p = 5\cdot x^{2} + 11\cdot x^{4}-9\cdot x^{15}+14\cdot x^{19}[/tex] and [tex]q = 12\cdot x^{22}[/tex], then we have:
[tex]p' = p+q[/tex]
[tex]p' = 5\cdot x^{2}+11\cdot x^{4}-9\cdot x^{15}+14\cdot x^{19}+12\cdot x^{22}[/tex]
The new expression is [tex]p' = 5\cdot x^{2}+11\cdot x^{4}-9\cdot x^{15}+14\cdot x^{19}+12\cdot x^{22}[/tex].
