show that (x-2),(x+3) and (x-4)are factors of x^3-x3x^2-10x+24 PLEASE HELP ME GUYS ☺
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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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