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Find ‘A‘ If the Two Polynomials Ax3 + 3x2 – 9 and 2x3 + 4x + A, Leave the Same Remainder When Divided by X + 3. - ICSE Class 10 - Mathematics

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Question

Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3. 

Solution

`x+3=0`  ⇒ `x=-3` 

Since, the given polynomials leave the same remainder when dividend by (x-3), 

value of polynomial `ax^3+3x^2-9` at x=-3  is sae as value of polynomial `2x^3+4x+a at x=-3` 

⇒  `a(-3)^3+3(-3)^2-9=2(-3)^3+4(-3)++a` 

⇒`-27a+27-9=-54-12+a` 

⇒`-27a+18=-66+a` 

⇒`28a=84` 

⇒`a=84/28` 

⇒a=3

 

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Solution Find ‘A‘ If the Two Polynomials Ax3 + 3x2 – 9 and 2x3 + 4x + A, Leave the Same Remainder When Divided by X + 3. Concept: Remainder Theorem.
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