what is the remainder when $(x^{4}+36)$ is divided by $(x^{2}-8)$?\n36\n64\n100\n117

Answer:

C. 100

Explanation:

Step1: Set up polynomial long - division

Let's divide (x^{4}+36) by (x^{2}-8). We know that (x^{4}\div x^{2}=x^{2}).

Step2: Multiply and subtract

Multiply (x^{2}-8) by (x^{2}) to get (x^{4}-8x^{2}). Then ((x^{4}+36)-(x^{4}-8x^{2}) = 8x^{2}+36).

Step3: Divide the new leading term

(8x^{2}\div x^{2}=8).

Step4: Multiply and subtract again

Multiply (x^{2}-8) by (8) to get (8x^{2}-64). Then ((8x^{2}+36)-(8x^{2}-64)=100). So the remainder is 100.