Question

Is x – 3 a factor of 5x5 – 3x4 + 2x2 – 9x + 12 ?

Answer 1

see explanation

Explanation:

If (x - 3) is a factor of the polynomial then f(3) = 0

Given

f(x) = 5
`x^(5)` - 3
`x^(4)` + 2x² - 9x + 12 , then

f(3) = 5
`(3)^(5)` - 3
`(3)^(4)` + 2(3)² - 9(3) + 12

= 5(243) - 3(81) + 2(9) - 27 + 12

= 1215 - 243 + 18 - 27 + 12 = 975

Since f(3) ≠ 0 then (x - 3) is not a factor of the polynomial

Answer 2

No

Explanation: