Question

Factorize this polynomial..it's urgent!!!​

Answer 1

Step-by-step explanation:

You can use long division. Another way is as follows:

x2+1x2−5x+6=(x2−5x+6)+(5x−5)x2−5x+6=x2−5x+6x2−5x+6+5x−5x2−5x+6=1+5x−5x2−5x+6

As next step notice that

x2−5x+6=(x−2)(x−3)

and expand in partial fractions:

5x−5x2−5x+6=Ax−2+Bx−3Where A and B are constants

You can use long division. Another way is as follows:

x2+1x2−5x+6=(x2−5x+6)+(5x−5)x2−5x+6=x2−5x+6x2−5x+6+5x−5x2−5x+6=1+5x−5x2−5x+6

As next step notice that

x2−5x+6=(x−2)(x−3)

and expand in partial fractions:

5x−5x2−5x+6=Ax−2+Bx−3Where A and B are constants

x2+1x2−5x+6=(x2−5x+6)+5(x−1)x2−5x+6

=1+5x−1x2−5x+6

⟹x−1x2−5x+6=x−1(x−2)(x−3)

=Ax−2+Bx−3

By comparing the corresponding coefficients, we get A=−1, B=2, hence

x−1x2−5x+6=−1x−2+2x−3

Hence, we have

x2+1x2−5x+6=1−5x−2+10x−3