Polynomials Help (1 Viewer)

[copynpaste]

I'm having troubles working out this question:

Find a and b if x^4-2x^3+x^2+ax+b is exactly divisible by x^2+x-1

What would you do to D(x)=x^2+x-1 (since D(x) cannot be factorised straight away, and nothing can be subbed into D(x) to equal zero... :/)?

 

[andybandy]

is the answer a = 10 and b = -6 ?

Edit: woops error in my working, and like trebla said, a = 8 and b = -5 although i did a different approach
note i long divided
<a href="http://www.codecogs.com/eqnedit.php?latex=x^{2}&plus;x-1&space;\textup{&space;by&space;}&space;x^{4}-2x^{3}&plus;x^{2}&plus;ax&plus;b&space;\textup{&space;and&space;got&space;}&space;x(a-8)&plus;b&plus;5" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x^{2}&plus;x-1&space;\textup{&space;by&space;}&space;x^{4}-2x^{3}&plus;x^{2}&plus;ax&plus;b&space;\textup{&space;and&space;got&space;}&space;x(a-8)&plus;b&plus;5" title="x^{2}+x-1 \textup{ by } x^{4}-2x^{3}+x^{2}+ax+b \textup{ and got } x(a-8)+b+5" /></a>

simply sub what would give the value 0 since their should be no remainder

 

[Trebla]

I'm having troubles working out this question:

Find a and b if x^4-2x^3+x^2+ax+b is exactly divisible by x^2+x-1

What would you do to D(x)=x^2+x-1 (since D(x) cannot be factorised straight away, and nothing can be subbed into D(x) to equal zero... :/)?

Noting that the polynomial is monic, suppose that:




Note you can also do this using a 4U approach and finding the complex roots of the factor.