Question

The quotient of (x4 – 3x2 + 4x – 3) and a polynomial is (x2 + x – 3). What is the polynomial?

A:x4 – 2x2 + 5x – 6
B: x2 – x + 1
C: x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9
D: x4 – 4x2 + 3x

Answer 1

x2 – x + 1

Explanation:

if

(x4 – 3x2 + 4x – 3)/ p(x) =(x2 + x – 3),

then

(x4 – 3x2 + 4x – 3)/(x2 + x – 3)= p(x)

(x4 – 3x2 + 4x – 3)/(x2 + x – 3)=x2 – x + 1

to check this we can multiply

(x2 + x – 3)*(x2 – x + 1)=

(x2 + x – 3)*x2 - (x2 + x – 3)*(x) + (x2 + x – 3)*1=

x4+x3-3x2-x3-x2+3x+x2+8-3= x4 – 3x2 + 4x – 3

Answer 2

x/y=z
if we know x and z

solve for y
x/y=z
times both sides by y
x=zy
divide both sides by z
x/z=y

therefor
(x^4– 3x2 + 4x – 3)/?=(x^2+x-3)
so

`(x^4-3x2 + 4x-3)/(x^2+x-3)`=?
solve
first factor them

`((x^2+x-3)(x^2-x+1))/(x^2+x-3)`=?
x^2-x+1=?
the poly is x^2-x+1