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Factrois ofx(x+ 3)+ 5(x+3) |
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Answer» -step EXPLANATION:AnswerGiven, (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)+24F(2)=8−12−20+24f(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)+24f(−3)=−27−27+30+24f(−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)+24f(4)=64−48−40+24f(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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