Question

Perform the indicated operation on thefollowing polynomials: (6x5 + 3x³ - 2) - (2x5 - 6x³ +7)

Answer 1

To effetuate addition or subtraction of polynomials, we just have to realize the operation with the coefficients of the corresponding degree.

`\begin{gathered} P(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0 \\ Q(x)=b_nx^n+b_(n-1)x^(n-1)+...+b_2x^2+b_1x+b_0 \\ P(x)-Q(x)=(a_n-b_n)x^n+(a_(n-1)-b_(n-1))x^(n-1)+...+(a_2-b_2)x^2+(a_1-b_1)x+(a_0-b_0) \end{gathered}`

Then, performing the given operation, we have:

`\begin{gathered} (6x^5+3x^3-2)-(2x^5-6x^3+7) \\ =6x^5+3x^3-2-2x^5+6x^3-7 \\ =(6-2)x^5+(3-2)x^3+(-2-7) \\ =4x^5+x^3-9 \end{gathered}`

Thus, this is our answer

`(6x^5+3x^3-2)-(2x^5-6x^3+7)=4x^5+x^3-9`