Keywords:
polynomial, coefficients, simplify, similar terms
For this case we have to simplify a polynomial, we must find the incognito coefficients of the variable "x" and the independent term. 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: They are the coefficients of the polynomial
n, n-1, 3,2,1,0: They are the exponents. And "n" represents the degree of the polynomial, because it is the largest exponent.
x: It is the variable.
So, if we have:
[tex]Q (x) = 8x ^ 2 - 8x + 2 - 5 + x[/tex]
To simplify, we must add similar terms, taking into account that different signs are subtracted and the sign of the major is placed.
[tex]Q (x) = 8x ^ 2-8x + x + 2-5\\Q (x) = 8x ^ 2-7x-3[/tex]
If we compare with the given simplified polynomial, we have:
[tex]8x ^ 2 - gx - h[/tex]
So we have [tex]g = 7\ and\ h = 3.[/tex]
[tex]8x ^ 2- (7) x - (3) = Q (x) = 8x ^ 2-7x-3[/tex]
Answer:
[tex]g = 7\ and\ h = 3[/tex]
