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6.5E: Mazoezi

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    176077

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    Mazoezi hufanya kamili

    Kutambua na Tumia Njia sahihi ya Kufanya Kipolynomial Kikamilifu

    Katika mazoezi yafuatayo, factor kabisa.

    1. \(2n^2+13n−7\)

    Jibu

    \((2n−1)(n+7)\)

    2. \(8x^2−9x−3\)

    3. \(a^5+9a^3\)

    Jibu

    \(a^3(a^2+9)\)

    4. \(75m^3+12m\)

    5. \(121r^2−s^2\)

    Jibu

    \((11r−s)(11r+s)\)

    6. \(49b^2−36a^2\)

    7. \(8m^2−32\)

    Jibu

    \(8(m−2)(m+2)\)

    8. \(36q^2−100\)

    9. \(25w^2−60w+36\)

    Jibu

    \((5w−6)^2\)

    10. \(49b^2−112b+64\)

    11. \(m^2+14mn+49n^2\)

    Jibu

    \((m+7n)^2\)

    12. \(64x^2+16xy+y^2\)

    13. \(7b^2+7b−42\)

    Jibu

    \(7(b+3)(b−2)\)

    14. \(30n^2+30n+72\)

    15. \(3x^4y−81xy\)

    Jibu

    \(3xy(x−3)(x^2+3x+9)\)

    16. \(4x^5y−32x^2y\)

    17. \(k^4−16\)

    Jibu

    \((k−2)(k+2)(k^2+4)\)

    18. \(m^4−81\)

    19. \(5x5y^2−80xy^2\)

    Jibu

    \(5xy^2(x^2+4)(x+2)(x−2)\)

    20. \(48x^5y^2−243xy^2\)

    21. \(15pq−15p+12q−12\)

    Jibu

    \(3(5p+4)(q−1)\)

    22. \(12ab−6a+10b−5\)

    23. \(4x^2+40x+84\)

    Jibu

    \(4(x+3)(x+7)\)

    24. \(5q^2−15q−90\)

    25. \(4u^5v+4u^2v^3\)

    Jibu

    \(u^2(u+1)(u^2−u+1)\)

    26. \(5m^4n+320mn^4\)

    27. \(4c^2+20cd+81d^2\)

    Jibu

    mkuu

    28. \(25x^2+35xy+49y^2\)

    29. \(10m^4−6250\)

    Jibu

    \(10(m−5)(m+5)(m^2+25)\)

    30. \(3v^4−768\)

    31. \(36x^2y+15xy−6y\)

    Jibu

    \(3y(3x+2)(4x−1)\)

    32. \(60x^2y−75xy+30y\)

    33. \(8x^3−27y^3\)

    Jibu

    \((2x−3y)(4x^2+6xy+9y^2)\)

    34. \(64x^3+125y^3\)

    35. \(y^6−1\)

    Jibu

    \((y+1)(y−1)(y^2−y+1)\)

    36. \(y^6+1\)

    37. \(9x^2−6xy+y^2−49\)

    Jibu

    \((3x−y+7)(3x−y−7)\)

    38. \(16x^2−24xy+9y^2−64\)

    39. \((3x+1)^2−6(3x−1)+9\)

    Jibu

    \((3x−2)2\)

    40. \((4x−5)^2−7(4x−5)+12\)

    Mazoezi ya kuandika

    41. Eleza nini maana ya kuzingatia polynomial kabisa.

    Jibu

    Majibu yatatofautiana.

    42. Tofauti ya mraba\(y^4−625\) inaweza kuzingatiwa kama\((y^2−25)(y^2+25)\). Lakini sio sababu kabisa. Nini zaidi lazima ifanyike kwa sababu kabisa.

    43. Ya mbinu zote factoring kufunikwa katika sura hii (GCF, kambi, tengua FOIL, 'ac' njia, bidhaa maalum) ambayo ni rahisi kwa ajili yenu? Ambayo ni ngumu zaidi? Eleza majibu yako.

    Jibu

    Majibu yatatofautiana.

    44. Kujenga tatu factoring matatizo ambayo itakuwa nzuri mtihani maswali kupima maarifa yako ya factoring. Onyesha ufumbuzi.

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili lina nguzo 4, mstari wa 1 na mstari wa kichwa. Mstari wa kichwa huandika kila safu: Naweza, kwa ujasiri, kwa msaada fulani na hapana, siipati. Safu ya kwanza ina taarifa ifuatayo: kutambua na kutumia njia sahihi ya kuzingatia polynomial kabisa. Nguzo zilizobaki ni tupu.

    b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?