A basic question from factorisation in which we are to find the value of X from given polynomial
ML Aggarwal Avichal Publication Factorisation chapter 6 Question no 2(ii)
Rajan@2021Guru
Using remainder theorem, find the remainder on dividing f(x) by (x+3) where f(x)=3x 3 +7x 2 −5x+1
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We know that the remainder theorem states that if a polynomial f(x) is divided by (x−a), the remainder is f(a).
Here, we have the polynomial f(x)=3x
3
+7x
2
−5x+1 which is divided by (x+3), therefore, by remainder theorem, the remainder is:
R=f(−3)=3(−3)
3
+7(−3)
2
−5(−3)+1=(3×−27)+(7×9)+15+1=−81+63+15+1=79−51=3
Hence, the remainder is −3.