An important question from factorisation in which we have to find what number must be subtracted from given polynomial 2x 3 −7x 2 +2x by applying remainder theorem
ML Aggarwal Avichal Publication Factorisation chapter 6, question no 7(ii)
Rajan@2021Guru
What number must be added to 2x 3 −7x 2 +2x so that the resulting polynomial leaves the remainder −2 when divided by 2x−3?
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Let
f(x)=2×3–7×2+2x
And p must be added to f(x)
∴f
′
(x)=2×3–7×2+2x+p
Dividing f(x) by 2x−3 by long division method, we get
2×3–7×2+2x+p=(2x−3)(x2−2x−2)+(p−6)
Hence, remainder is p–6
⇒p−6=−2[given, remainder =−2]
⇒p=−2+6
⇒p=4
Therefore, 4 is to be added