Q. Polynomial remainder transformations (1 Viewer)

[ezzy85]

A monic cubic poly when divided by x² - 9 leaves a remainder of x + 8 and when divided by x leaves a remainder of -4. Express the poly in the form ax³ + bx² + cx + d.

Thanks

 

[OLDMAN]

Work with monic and P(x)=Q(x)D(x)+R(x),
x^3+Ax^2+Bx+C=Q(x)D(x)+R(x)

You will get 3 eqns. to solve for A,B, and C substituting x=3,-3 and 0.

 

[Constip8edSkunk]

let p(x)=x^3+ax^2+bx+d
p(0)=-4 so d=-4

(x^3+ax^2+bx-4)/(x^2-9)=(x+a)+[(b+9)x+9a-4]

equating the coefficients of the remainder {as (b+9)x+9a-4 = x=8}:

b+9=1 b=-8
9a-4=8 a=4/3

p(x)=x^3+(4/3)x^2-8x-4
= 3x^3+4x^2-24x-12

 

[bobo123]

sorry skunk, im crappo at poly and i dont get your answer

mind spoon feeding it to me ?


cheers

 

[Constip8edSkunk]

yah i messed up a bit on the equations, now editted

 

[bobo123]

yep i get the same answer now

1 question
is it suppose to be left in monic or do we make it nice (no fractions)?

 

[ezzy85]

cool, thanks