Question

Use the remainder theorem to determine the remainder. Then use the remainder to determine if the binomial is the factor of a polynomial. f(x) = x^3 + x^2 - 66x + 54 is divided by x + 9.

a. Remainder: 0; not a factor
b. Remainder: 0; yes a factor
c. Remainder: 270; not a factor
d. Reaminder:270; yes a factor

Answer 1

b

Explanation:

If (x + h) is a divisor of f(x) then f(- h) = remainder

If f(- h) = 0 then (x + h) is a factor of f(x)

Here divisor is (x + 9) , then

f(- 9) = (- 9)³ + (- 9)² - 66(- 9) + 54

= - 729 + 81 + 594 + 54

= 0

Thus remainder is 0 and (x + 9) is a factor of f(x)

Answer 2

b

Explanation:

f(x) = x³ + x² - 66x + 54

= (x² - 8x + 6)(x + 9) + 0

=> the answer is b