Respuesta :
A polynomial is a function that, given an input [tex] x [/tex], returns as output a sum of powers of [tex] x [/tex], each multiplied by some coefficient. Note that 1 is a power of [tex] x [/tex], since [tex] x^0=1 [/tex]
The degree of the polynomial is the highest exponent of [tex] x [/tex] appearing in the sum.
So. if you want to build a polynomial with degree 3 or higher, you have to:
1 - Choose the degree of the polynomial to be 3 or higher, for example 5.
2 - Consider all the powers of [tex] x [/tex], with exponents up to 5: [tex] 1,x,x^2,x^3,x^4,x^5 [/tex]
3- Assing a coefficient to every power. We usually write [tex] a_n [/tex] to indicate the coefficient of [tex] x^n [/tex]. You can choose any number you like. So, for example, you can choose
[tex] a_0 = 3, a_1 = 0, a_2 = -5, a_3 = 12, a_4 = -1, a_5 = 1 [/tex]
4 - Multiply each power by its coefficient, and sum all the pieces:
[tex] a_0x^0 + a_1x^1 + a_2x^2 + a_3x^3 + a_4x^4 + a_5x^5 [/tex]
[tex] 3\cdot 1 + 0\cdot x^1 + (-5)\cdot x^2 + 12\cdot x^3 + (-1)\cdot x^4 + 1\cdot x^5 [/tex]
[tex] 3 -5x^2 + 12x^3 -x^4 + x^5 [/tex]
