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Phân tích các đa thức sau thành nhân tử : a) x√x + √x – x – 1 b) √ab + 2√a + 3√b + 6 c) 3√a – 2a – 1 d) 4a – 4√a – 1 e) a√a + 2√ab + √a + 2√b f) x – 3
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Khải Quang
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Đáp án:
$\begin{array}{l}
a)x\sqrt x + \sqrt x – x – 1\\
= \sqrt x \left( {x + 1} \right) – \left( {x + 1} \right)\\
= \left( {x + 1} \right)\left( {\sqrt x – 1} \right)\\
b)\sqrt {ab} + 2\sqrt a + 3\sqrt b + 6\\
= \sqrt a \left( {\sqrt b + 2} \right) + 3\left( {\sqrt b + 2} \right)\\
= \left( {\sqrt b + 2} \right)\left( {\sqrt a + 3} \right)\\
c)3\sqrt a – 2a – 1\\
= 2\sqrt a + \sqrt a – 2a – 1\\
= 2\sqrt a \left( {1 – \sqrt a } \right) – \left( {1 – \sqrt a } \right)\\
= \left( {1 – \sqrt a } \right)\left( {2\sqrt a – 1} \right)\\
d)4a – 4\sqrt a – 1\\
= 4a – 4\sqrt a + 1 – 2\\
= {\left( {2\sqrt a + 1} \right)^2} – 2\\
= \left( {2\sqrt a + 1 + \sqrt 2 } \right)\left( {2\sqrt a + 1 – \sqrt 2 } \right)\\
e)a + 2\sqrt {ab} + \sqrt a + 2\sqrt b \\
= \sqrt a \left( {\sqrt a + 2\sqrt b } \right) + \left( {\sqrt a + 2\sqrt b } \right)\\
= \left( {\sqrt a + 2\sqrt b } \right)\left( {\sqrt a + 1} \right)\\
f)x – 3\sqrt x + 2\\
= \left( {\sqrt x – 2} \right)\left( {\sqrt x – 1} \right)\\
g)x + 4\sqrt x + 3\\
= \left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right)
\end{array}$
Đáp án:
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