Polynomials (1 Viewer)

[FDownes]

More maths trouble, this time with polynomials;

A polynomial P(x) = (x - b)⁷ Q(x)

a) Show that P(b) = P'(b) = 0

This first part is pretty easy, but it's the second part I'm not sure about...

b) Hence find a and b if (x - 1)⁷ is a factor of x⁷ + 3x⁶ + ax⁵ + x⁴ + 3x³ + bx² - x - 1

Who can help me out of this one?

 

[tommykins]

a) is simple

b) Sub in x = 1 for P(x) and you get an equation with a and b.
Then sub x = 1 for P'(x) and you get another equation. => Simulateneous equations.

Note that (x-1)^7 is a factor therefore its multiplicty is 7.

 

[FDownes]

Man, I should have seen that myself. For some reason I didn't make the connection between using the first part of the question in the solution to the second...

 

[tommykins]

If q's come in parts, you wuold assume most of it is a "Hence".