Toán Lớp 8: cho A(x) = x mũ 3 + ax + b
B(x) = x mũ 2 + x – 2
tìm a,b để A chia hết cho B
cần gấp
đặt tính
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Toán Lớp 8: cho A(x) = x mũ 3 + ax + b
B(x) = x mũ 2 + x – 2
tìm a,b để A chia hết cho B
cần gấp
đặt tính
Comments ( 1 )
A\left( x \right) = {x^3} + a.x + b\\
= {x^3} + {x^2} – 2x – {x^2} – x + 2\\
+ 3x + a.x + b – 2\\
= x\left( {{x^2} + x – 2} \right) – \left( {{x^2} + x – 2} \right)\\
+ \left( {3 + a} \right).x + b – 2\\
= \left( {{x^2} + x – 2} \right)\left( {x – 1} \right) + \left( {3 + a} \right).x + b – 2\\
Do:\left( {{x^2} + x – 2} \right)\left( {x – 1} \right) \vdots \left( {{x^2} + x – 2} \right)\\
Khi:A\left( x \right) \vdots B\left( x \right)\\
\Leftrightarrow \left( {3 + a} \right).x + b – 2 = 0\\
\Leftrightarrow \left\{ \begin{array}{l}
3 + a = 0\\
b – 2 = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = – 3\\
b = 2
\end{array} \right.\\
Vậy\,a = – 3;b = 2
\end{array}$