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≪因数分解≫ 【解説】(問題は下にあります.) ■ 次の公式を使って因数分解するときは,はじめに両端を見るのがヒケツです.真ん中は最後に見ます.
○ 2乗になる例 x2+6x+9=x2+6x+32 (ここで 2·3x=6x を確かめる) =(x+3)2 ○ 2乗にならない例 x2+6x+16=x2+6x+42 (ここで 2·4x は 6x でない) ・・・ (→2乗にならない) ○ 前から順に見ていくと,次の違いが分らなくても,両端から見て,「最後に真ん中で確認する」と分かります.
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■ 次の因数分解をしなさい.(解答欄から正しいものを選びなさい) | ||
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16=42.そこでx2+2×4×x+42とするとx2+8x+16に等しくなるから,x2+8x+16=(x+4)2が成り立つ. | ||
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9=32.そこでx2−2×3×x+32とするとx2−3x+9にならないから,与えられた問題は「2乗にならない」. | ||
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4=22.そこでx2+2×2×x+22とするとx2+4x+4に等しくなるから,x2+4x+4=(x+2)2が成り立つ. | ||
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8=(2![]() ![]() ![]() |
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36=62.そこでx2−2×6×x+62とするとx2−12x+36に等しくなるから,x2−12x+36=(x−6)2が成り立つ. |
次の空欄を埋めなさい. |
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25=52 , 2×5=10だからx2+10x+25=(x+5)2が成り立つ. | |
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49=72 , 2×7=14だからx2−14x+49=(x−7)2が成り立つ. | |
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9=32 , 2×3=6だからx2+6x+9=(x+3)2が成り立つ. | |
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36=62 , 2×6=12だからx2+12x+36=(x+6)2が成り立つ. | |
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9=32 , 16=42 , 2×4×3=24だから16x2−24x+9=(4x−3)2が成り立つ. |
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