Question

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Answer 1

Answer:

HERE THE MAXIMUM POWER OF X IS 3 SO THAT IT CAN HAVE MAXIMUM 3 FACTORS

Step-by-step explanation:

LET TAKE F(X)=$x^{3}$+2$x^{2}$-X-2

THE CONSTANT TERM IN F(X) IS +/-1 AND +/-2

PUTTING X=1 IN F(X),WE HAVE

F(1)=$1^{3}$-2*$1^{2}$-1-2

=1+2-1-2=0

ACCORDING TO REMINDER THEOREM F(1)=0 SO THAT (X-1) IS A FACTOR OF $x^{3}$+2$x^{2}$-X-2

PUTTING X=-1 IN F(X) ,WE HAVE

F(-1)=-1^{3}+2*(-1)^2-(-1)-2

-1-2+1+2=0

(X+1) IS A FACTOR OF X^3+2X^2-X-2

PUTTING X=2 IN F(X),WE HAVE

F(-2)=(-2)^3+2(-2)^2-(-2)-2

=-8+8-2+2=0

F(2)=0,SO THAT (X-2) IS FACTOR OF X^3+2X^2-2-2

HERE THE MAXIMUM POWER OF X IS 3 SO THAT IT CAN HAVE MAXIMUM 3 FACTORS

Answer 2

Answer:

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