Answer:
see explanation
Step-by-step explanation:
given (x - 5) is a factor of f(x) then x = 5 is a zero
dividing f(x) by (x - 5) using synthetic division
5 | 1 - 8 17 - 10
↓ 5 - 15 10
----------------------
1 - 3 2 0 ← remainder = 0 indicates (x - 5) is a factor
quotient = x² - 3x + 2 = (x - 1)(x - 2)
then
f(x) = (x - 5)(x - 1)(x - 2) ← in factored form
to find the x- intercepts let f(x) = 0 , that is
(x - 5)(x - 1)(x - 2) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
the x- intercepts are x = 1, x = 2, x = 5
to find the y- intercept let x = 0 , then
f(0) = (0 - 5)(0 - 1)(0 - 2) = (- 5)(- 1)(- 2) = 5 × - 2 = - 10
the y- intercept is y = - 10
