magdalenovalde
Answered

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

Verified Answer :

apologiabiology

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
\(\frac{x^4-3x2 + 4x-3}{x^2+x-3}\)=?
solve
first factor them
\(\frac{(x^2+x-3)(x^2-x+1)}{x^2+x-3}\)=?
x^2-x+1=?
the poly is x^2-x+1




mvelazcoa

Answer:

x2 – x + 1

Step-by-step 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