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2 months ago

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

Mathematics

2 answers:

Leona [12.6K]2 months ago

7 0

8x²-8x+2-5+x reduces to 8x² - 7x - 3
Therefore, we find g = 7 and h = 3

PIT_PIT [12.4K]2 months ago

6 0

Key Terms:

polynomial, coefficients, simplification, like terms

In this situation, simplifying a polynomial requires identifying the unknown coefficients for "x" and the constant term. By definition, a polynomial has the structure:

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

a, b, c, d, e, and f signify the coefficients.

n, n-1, 3, 2, 1, 0 are the respective exponents, and "n" denotes the degree of the polynomial due to being the largest exponent.

x is the variable in question.

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

To simplify, it's necessary to combine like terms, keeping in mind that opposite signs result in subtraction while the dominant sign prevails.

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

Comparing to the provided simplified polynomial yields:

$8x ^ 2 - gx - h$

Hence we conclude with $g = 7\ and\ h = 3.$

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

Conclusion:

$g = 7\ and\ h = 3$

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