Question

What is the quotient and remainder when dividing the polynomial (x³+2x+1)/(x²-x+3)

a) Quotient: x+3, Remainder: −x+10
b) Quotient: x+3, Remainder: −x−10
c) Quotient: x−3, Remainder: x+10
d) Quotient: −x+3, Remainder: x−10

Answer 1

To divide the polynomial (x³+2x+1) by (x²-x+3), use polynomial long division to get the quotient and remainder.

Step-by-step explanation:

To divide (x³+2x+1) by (x²-x+3), we can use polynomial long division.

Step 1: Divide the first term of the dividend (x³) by the first term of the divisor (x²) to get x.

Step 2: Multiply the entire divisor (x²-x+3) by the quotient found in Step 1 (x), and subtract the result from the dividend (x³+2x+1).

Step 3: Repeat steps 1 and 2 for the resulting polynomial until the degree of the remaining polynomial is less than the degree of the divisor.

After performing the long division, we get:

Quotient: x+3

Remainder: -x-10