Question

Is (r-4) a factor of 6r^4-17r^3-46r^2+77r-20? What are the steps and how would you know if it’s a factor?

Answer 1

see explanation

Explanation:

By the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

if (r - 4) is a factor then substituting r = 4 into the polynomial should result in it having a value of zero, that is

6
`r^(4)` - 17r³ - 46r² + 77r - 20 ( substitute r = 4 )

= 6
`(4)^(4)` - 17(4)³ - 46(4)² + 77(4) - 20

= 6(256) - 17(64) - 46(16) + 308 - 20

= 1536 - 1088 - 736 + 288

= 0

Then (r - 4) is a factor of the polynomial