In Exercises use synthetic division to perform the indicated division. Write the polynomial in the form p(x) = d(x)q(x) + r(x) (x^(2) - 5) ÷ (x-5)

Question

In Exercises use synthetic division to perform the indicated division. Write the polynomial in the form

p(x) = d(x)q(x) + r(x)


`(x^(2) - 5)` ÷
`(x-5)`

Answer 1

p(x) = (x - 5)(x + 5) + 20

Explanation:

(x² - 5) ÷ (x - 5) ⇒ we put zero in place of x in the dividend

(x² + 0 - 5) ÷ (x - 5) = x + (5x - 5) ÷ (x - 5)

= (x + 5) + 20 ÷ (x - 5)

The quotient = (x + 5) ⇒ q(x)

The remainder = 20 ⇒ r(x)

The divisor = (x - 5) ⇒ d(x)

∴ p(x) = (x - 5)(x + 5) + 20