Question

Divide x^3 + 2x^2 – 5x – 10 by x^2 – 5 using long division. Show all work.

x – 10

x + 2

x + 2 R. –20

Answer 1

Divide (x^3 + 2x^2 − 5x − 10) by (x^2 − 5):

1. Leading term: x^3 ÷ x^2 = x.
Multiply: x(x^2 − 5) = x^3 − 5x.
Subtract: (x^3 + 2x^2 − 5x − 10) − (x^3 − 5x) = 2x^2 + 0x − 10.

2. Next term: 2x^2 ÷ x^2 = 2.
Multiply: 2(x^2 − 5) = 2x^2 − 10.
Subtract: (2x^2 − 10) − (2x^2 − 10) = 0.

Remainder = 0, so the quotient is x + 2.

Check: (x^2 − 5)(x + 2) = x^3 + 2x^2 − 5x − 10.