7. Show that x + x + 1 is not a factor of the expression
x* – 4x° +x? -5x + 6.​

1 thought on “7. Show that x + x + 1 is not a factor of the expression<br />x* – 4x° +x? -5x + 6.​”

1. Answer:

   Given, (x−2) , (x+3) and (x−4) are factors of polynomial x

   3

   −3x

   2

   −10x+24.

   Then, f(x)=x

   3

   −3x

   2

   −10x+24.

   If (x−2) is a factor, then x−2=0⟹x=2.

   Replace x by 2, we get,

   f(2)=(2)

   3

   −3(2)

   2

   −10(2)+24

   f(2)=8−12−20+24

   f(2)=0.

   The value of f(2) is zero.

   Then (x−2) is the factor of the polynomial x

   3

   −3x

   2

   −10x+24.

   If (x+3) is factor, then x+3=0⟹x=−3.

   Replace x by −3, we get,

   f(−3)=(−3)

   3

   −3(−3)

   2

   −10(−3)+24

   f(−3)=−27−27+30+24

   f(−3)=0.

   The value of f(−3) is zero.

   Then (x+3) is the factor of the polynomial x

   3

   −3x

   2

   −10x+24.

   If (x−4) is factor, then x−4=0⟹x=4.

   Replace x by 4, we get,

   f(4)=(4)

   3

   −3(4)

   2

   −10(4)+24

   f(4)=64−48−40+24

   f(4)=0.

   The value of f(4) is zero.

   Then (x+4) is the factor of the polynomial x

   3

   −3x

   2

   −10x+24.

   Therefore, hence showed that (x−2) , (x+3) and (x−4) are factors of polynomial x

   3

   −3x

   2

   −10x+24.

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