phân tích đa thức thanhf nhân tử
1) (x+1)(x+3)(x+5)(x+7)-24
2) (x mũ 2+4x+8) mũ 2+3x( x mũ 2+4x+8)+2x mũ 2
3) (x mũ 2+8x+7)(x mũ 2+8x+15)+15
4) (x mũ 2+x+1)(x mũ 2+x+2)-12
hộ mik với mik cần gấp
phân tích đa thức thanhf nhân tử
1) (x+1)(x+3)(x+5)(x+7)-24
2) (x mũ 2+4x+8) mũ 2+3x( x mũ 2+4x+8)+2x mũ 2
3) (x mũ 2+8x+7)(x mũ 2+8x+15)+15
4) (x mũ 2+x+1)(x mũ 2+x+2)-12
hộ mik với mik cần gấp
Đáp án:
$\begin{array}{l}
1)A = \left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 5} \right)\left( {x + 7} \right) – 24\\
= \left( {x + 1} \right)\left( {x + 7} \right)\left( {x + 3} \right)\left( {x + 5} \right) – 24\\
= \left( {{x^2} + 8x + 7} \right)\left( {{x^2} + 8x + 15} \right) – 24\\
\text{Đặt}:{x^2} + 8x + 7 = a\\
\Rightarrow A = a\left( {a + 8} \right) – 24\\
= {a^2} + 8a – 24\\
= {a^2} + 8a + 16 – 40\\
= {\left( {a + 4} \right)^2} – {\left( {2\sqrt {10} } \right)^2}\\
= \left( {a + 4 + 2\sqrt {10} } \right)\left( {a + 4 – 2\sqrt {10} } \right)\\
= \left( {{x^2} + 8x + 7 + 4 + 2\sqrt {10} } \right)\\
.\left( {{x^2} + 8x + 7 + 4 – 2\sqrt {10} } \right)\\
= \left( {{x^2} + 8x + 11 + 2\sqrt {10} } \right).\left( {{x^2} + 8x + 11 – 2\sqrt {10} } \right)\\
2)B = {\left( {{x^2} + 4x + 8} \right)^2} + 3x\left( {{x^2} + 4x + 8} \right) + 2{x^2}\\
\text{Đặt}:\left\{ \begin{array}{l}
{x^2} + 4x + 8 = a\\
x = b
\end{array} \right.\\
\Rightarrow B = {a^2} + 3ab + 2{b^2}\\
= \left( {a + b} \right)\left( {a + 2b} \right)\\
= \left( {{x^2} + 4x + 8 + x} \right).\left( {{x^2} + 4x + 8 + 2x} \right)\\
= \left( {{x^2} + 5x + 8} \right).\left( {{x^2} + 6x + 8} \right)\\
3)C = \left( {{x^2} + 8x + 7} \right)\left( {{x^2} + 8x + 15} \right) + 15\\
\text{Đặt}:{x^2} + 8x + 7 = a\\
\Rightarrow C = a\left( {a + 8} \right) + 15\\
= {a^2} + 8a + 15\\
= \left( {a + 3} \right)\left( {a + 5} \right)\\
= \left( {{x^2} + 8x + 7 + 3} \right).\left( {{x^2} + 8x + 7 + 5} \right)\\
= \left( {{x^2} + 8x + 10} \right).\left( {{x^2} + 8x + 12} \right)\\
4)D = \left( {{x^2} + x + 1} \right)\left( {{x^2} + x + 2} \right) – 12\\
{x^2} + x + 1 = a\\
\Rightarrow D = a\left( {a + 1} \right) – 12\\
= {a^2} + a – 12\\
= \left( {a + 4} \right)\left( {a – 3} \right)\\
= \left( {{x^2} + x + 1 + 4} \right).\left( {{x^2} + x + 1 – 3} \right)\\
= \left( {{x^2} + x + 5} \right).\left( {{x^2} + x – 2} \right)
\end{array}$