Question

Help on (b) pleasea level maths factor theorem ​

Answer 1

Step-by-step explanation:

According to factor theorem, if x − c is a factor of f(x), then f(c) = 0.

Conversely, if f(c) = 0, then x −c is a factor of f(x).

a) If x − 3 is a factor of f(x), then f(3) will be 0.

f(3) = 4(3)³ − 12(3)² + 2(3) − 6

f(3) = 0

b) Having shown that x − 3 is a factor of f(x), we can use grouping or long division to factor f(x):

f(x) = 4x³ − 12x² + 2x − 6

f(x) = 4x² (x − 3) + 2 (x − 3)

f(x) = (4x² + 2) (x − 3)

Since 4x² + 2 has only imaginary zeros, 3 is the only real root.