Question

Add (3x4 − 2x3 + 1) + (12x4 + x2 − 11)

Answer 1

`15x^(4) -2x^(3) +x^(2) -10`

Explanation:

Answer 2

For this case we have that by definition, a polynomial is of the form:

`P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f`

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:

`Q (x) = 3x ^ 4-2x ^ 3 + 1\\R (x) = 12x ^ 4 + x ^ 2-11`

Both polynomials are grade 4.

To add them we do the following:

1. We complete the polynomials:

`Q (x) = 3x ^ 4-2x ^ 3 + 0x ^ 2 + 0x + 1\\R (x) = 12x ^ 4 + 0x ^ 3 + x ^ 2 + 0x-11`

2. Let's add similar terms, that is:

`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`

Answer:

The sum of the given polynomials is:
`15x ^ 4-2x ^ 3 + x ^ 2-10`