Question

'show that (x-2), (x+3) and
(x-4) are factors of
X3-3x2-10x+24​

Answer 1

Answer:

Given (x-2) ,(x+3) and (x-4) is factor of polynomial x

3

−3x

2

−10x+24

If (x-2) is factor x-2=0 or x=2

Replace x by 2 we get

f(2)=x

3

−3x

2

−10x+24

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 x

3

−3x

2

−10x+24

If (x+3) is factor x+3=0 or x=-3

Replace x by -3we get

f(x)=x

3

−3x

2

−10x+24

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 x

3

−3x

2

−10x+24

If (x-4) is factor x-4=0 or x=4

Replace x by 4 we get

f(x)=x

3

−3x

2

−10x+24

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 x

3

−3x

2

−10x+24

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Answer 2

Step-by-step explanation:

Given (x-2) ,(x+3) and (x-4) is factor of polynomial x−3x2−10x+24

If (x-2) is factor x-2=0 or x=2

Replace x by 2 we get

f(2)=x 3 −3x 2−10x+24f(2)=(2) 3 −3(2) 2−10(2)+24f(2)=8−12−20+24f(2)=0

The value of f(2) is zero then (x-2) is the factor of x

3

−3x

2

−10x+24

If (x+3) is factor x+3=0 or x=-3

Replace x by -3we get

f(x)=x

3

−3x

2

−10x+24

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 x

3

−3x

2

−10x+24

If (x-4) is factor x-4=0 or x=4

Replace x by 4 we get

f(x)=x

3

−3x

2

−10x+24

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 x

3

−3x

2

−10x+24