Polynomial Question Help (: (1 Viewer)

[lisarh]

A monic cubic polynomial when divided by (x²+4) leaves a remainder of (x+8) and when divided by x leaves a remainder of -4.

Find the polynomial in the form ax³+bx²+cx+d.

 

[M@ster P]

are you sure its not (x^2 - 4) because it will make the question alot easier.

 

[samwell]

since the polynomial is monic a=1 therfore use long dovision to divide polynomial ax³+bx²+cx+d by (x²+4) and u should get the remainder as [c-4a]x +4b which is equal to x+8. now c-4a=1 and 4b=8 then solve the eqn bcoz u noe that a=1. hope that made sense

 

[lisarh]

are you sure its not (x^2 - 4) because it will make the question alot easier.

Yeah, the qu is (x^2+4), but it could be a typo on my sheet if you say so.

PS, hey! you go DLS, I'm from MSJ x]

 

[M@ster P]

hello

 

[samwell]

Yeah, the qu is (x^2+4), but it could be a typo on my sheet if you say so.

PS, hey! you go DLS, I'm from MSJ x]

read the definition of a monic polynomial.

 

[Rampager]

since the polynomial is monic a=1 therfore use long dovision to divide polynomial ax³+bx²+cx+d by (x²+4) and u should get the remainder as [c-4a]x +4b which is equal to x+8. now c-4a=1 and 4b=8 then solve the eqn bcoz u noe that a=1. hope that made sense

I think you miss a step


........... _ax_+_b_______
(x²+4)/ ax³+bx²+cx+d
.............ax³ + 4ax
....................bx²+cx+d - 4ax
....................bx² + 4b
r. cx + d - 4ax - 4b

Remainder = x[c-4a] + d - 4b = x + 8
c - 4 = 1 .............. d - 4b = 8
c = 5 .............. d - 4b = 8

To find d

Divide ax³+bx²+cx+d by x.
Remainder = d = -4

-4 -4b = 8
b = -3

Polynomial is: x³-3x²+5x-4

 

[samwell]

I think you miss a step


........... _ax_+_b_______
(x²+4)/ ax³+bx²+cx+d
.............ax³ + 4ax
....................bx²+cx+d - 4ax
....................bx² + 4b
r. cx + d - 4ax - 4b

Remainder = x[c-4a] + d - 4b = x + 8
c - 4 = 1 .............. d - 4b = 8
c = 5 .............. d - 4b = 8

To find d

Divide ax³+bx²+cx+d by x.
Remainder = d = -4

-4 -4b = 8
b = -3

Polynomial is: x³-3x²+5x-4

Thanks