Question

How do you use the remainder theorem to see if the `b-7` is a factor of `b^4-8b^3-b^2+62b-34`?

Answer 1

b - 7 is not a factor of said equation.

Explanation:

Here b - 7 = 0. So, b = 7. now put the value of b i.e. 7 in equation
`b^4 - 8b^3 - b^2 + 62b - 34`. If the equation becomes 0, then b - 7 will be one of the factor.
Hence,
`7^4 - 8* 7^3- 7^2 + 62*7` - 34
= 2401 - 2744 - 49 + 434 - 34
= 2835 - 2827
= 8
Therefore b - 7 is not a factor of said equation.