Question

find the gcd of the polynomial x3+x2-x+2;2x3-5x2+5x-3​

Answer 1

Answer:

Step-by-step explanation:

Let f(x)=x  

4

+3x  

3

+5x  

2

+26x and g(x)=x  

4

+2x  

3

−4x  

2

−x+28

Given that GCD =x  

2

+5x+7. Also, we have GCD × LCM= f(x) × g(x).

Thus, LCM=  

GCD

f(x)×g(x)

​  

 

Now, GCD divides both f(x) and g(x).

Let us divided f(X) by the GCD.

When f(x) is divided by GCD, we get the quoteint as x  

2

−2x+8.

Now, (1) → LCM =(x  

2

−2x+8)×g(x)

Thus, LCM =(x  

2

−2x+8)(x  

4

+2x  

3

−4x  

2

−x+28).