Question

(2xpower of 4-6xcube+3xsquare+3x-2)÷(xsquare-3x+2)plz slove this question​

Answer 1

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Answer 2

Answer:

The divisor is not a linear polynomial. It is a quadratic polynomial. Let us see factorization of a quadratic polynomial by splitting the middle term :

x2−3x+2

= x2−2x−x+2

= x(x−2)−1(x−2)

= (x−1)(x−2)

Then (x−1) and (x−2) are factor of polynomial x2−3x+2.

If (x−1) and (x−2) both are factors, then x=1 and x=2 gives zero polynomial.

p(x)=2x4−6x3+3x2+3x−2

On replacing x by 2, we get 

p(2)=2(2)4−6(2)3+3(2)2+3(2)−2

⇒p(2)=32−48+12+6−2=0

On replacing x by 1, we get

p(1)=2(1)4−6(1)3+3(1)2+3(1)−2

p(1)=2−6+3+3−2=0

So, (x−1) and (x−2) gives zero polynomial, then