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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. - 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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