Question

subtract these polynomials.

$(6x^2 - x + 8) - (x^2 + 2) =$

a. $5x^2 - x + 6$
b. $5x^2 - x + 10$
c. $7x^2 - x + 6$
d. $7x^2 - x + 10$

Explanation:

Step1: Distribute the subtraction

To subtract the polynomials, we first distribute the negative sign to the second polynomial:
$(6x^2 - x + 8) - (x^2 + 2) = 6x^2 - x + 8 - x^2 - 2$

Step2: Combine like terms

• For the $x^2$ terms: $6x^2 - x^2 = 5x^2$
• The $x$ term remains: $-x$ (since there are no other $x$ terms to combine)
• For the constant terms: $8 - 2 = 6$

Combining these results, we get $5x^2 - x + 6$.

Answer:

A. $5x^2 - x + 6$