Question

The polynomial 8x2 – 8x + 2 – 5 + x is simplified to 8x2 – gx – h. What are the value of g and h?

Answer 1

8x²-8x+2-5+x = 8x² - 7x - 3 
Thus, g = 7 and h = 3

Answer 2

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:

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

$Q (x) = 8x ^ 2 - 8x + 2 - 5 + x$

To simplify, we must add similar terms, taking into account that different signs are subtracted and the sign of the major is placed.

$Q (x) = 8x ^ 2-8x + x + 2-5\\Q (x) = 8x ^ 2-7x-3$

If we compare with the given simplified polynomial, we have:

$8x ^ 2 - gx - h$

So we have $g = 7\ and\ h = 3.$

$8x ^ 2- (7) x - (3) = Q (x) = 8x ^ 2-7x-3$

Answer:

$g = 7\ and\ h = 3$