Ax^3 +3x^2-13 and 2x^3-5x+2 have x-a as common factor ,find a

1.	Ax^3 +3x^2-13 and 2x^3-5x+2 have x-a as common factor ,find a
Answer» Let\xa0p(x) = ax3 + 3x2 - 13 and q(x) = 2x3 - 5x + a be the given polynomials.\xa0The remainders when p(x) and q(x) are divided by (x + 2) are p(- 2) and q(- 2) respectively.By the given condition, we havep(-\xa02) = q(-2){tex}\\Rightarrow{/tex}\xa0a(-2)3 + 3\xa0{tex}\\times{/tex} (-2 )2 - 13 = 2 {tex}\\times{/tex} (-2)3 - 5\xa0{tex}\\times{/tex} (-2) + a{tex}\\Rightarrow{/tex}\xa0-8a + 12 - 13 = - 16 + 10 + a\xa0{tex}\\Rightarrow{/tex}\xa0-8a - 1 = a - 6{tex}\\Rightarrow{/tex} -9a = - 5\xa0{tex}\\Rightarrow a=\\frac{5}{9}{/tex}

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