Question

(x+2) is a factor of mx^3+nx^2+x-6. it leaves the remainder 4 when divided by (x-2) find m and n

Answer 1

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Answer 2

Answer:

m=−3,n=−1

m=−3,n=−1x−2 is factor

m=−3,n=−1x−2 is factor ⇒x=2

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2n

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3⇒33+9m+3n=3

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3⇒33+9m+3n=3⇒10+3m+n=0⟶(ii)

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3⇒33+9m+3n=3⇒10+3m+n=0⟶(ii)From (i) & (ii)

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3⇒33+9m+3n=3⇒10+3m+n=0⟶(ii)From (i) & (ii)m=−3

m=−3,n=−1x−2 is factor ⇒x=2f(2)=14+4m+2nRemainder is zero⇒7+2m+n=0⟶(i)Now, x−3=0gives remainder 3⇒f(3)=3⇒33+9m+3n=3⇒10+3m+n=0⟶(ii)From (i) & (ii)m=−3n=−1