Answer:
see explanation
Explanation:
if (x - h) is a factor of f(x) then f(h) = 0
(a)
if (x - 2) is a factor of f(x) then f(2) = 0
f(2) = 2³ - 7(2) + 6
= 8 - 14 + 6
= - 6 + 6
= 0
since f(2) = 0 then (x - 2) is a factor of f(x)
(b)
using synthetic division to factor f(x)
insert a zero in the x² position on the table
2 | 1 0 - 7 6
↓ 2 4 - 6
-----------------------
1 2 - 3 0
quotient is
x² + 2x - 3 = (x + 3)(x - 1)
Then
f(x) = (x - 2)(x + 3)(x - 1)