For this case we have that by definition, a polynomial is of the form:
[tex]P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]
Where:
a, b, c, d, e, f are the polynomial coefficients
n, n-1,3,2,1,0 are the exponents. n is the largest, therefore represents the degree of the polynomial.
x is the variable
Given the following polynomials:
[tex]Q (x) = 3x ^ 4-2x ^ 3 + 1\\R (x) = 12x ^ 4 + x ^ 2-11[/tex]
Both polynomials are grade 4.
To add them we do the following:
1. We complete the polynomials:
[tex]Q (x) = 3x ^ 4-2x ^ 3 + 0x ^ 2 + 0x + 1\\R (x) = 12x ^ 4 + 0x ^ 3 + x ^ 2 + 0x-11[/tex]
2. Let's add similar terms, that is:
[tex]Q (x) + R (x) = (12 + 3) x ^ 4 + (- 2 + 0) x ^ 3 + (0 + 1) x ^ 2 + (0 + 0) x + (1-11)\\Q (x) + R (x) = 15x ^ 4-2x ^ 3 + x ^ 2 + 0x-10\\Q (x) + R (x) = 15x ^ 4-2x ^ 3 + x ^ 2-10[/tex]
Answer:
The sum of the given polynomials is: [tex]15x ^ 4-2x ^ 3 + x ^ 2-10[/tex]
