Sura ya 7 Mazoezi Mapitio
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- 177482
Sura ya 7 Mazoezi Mapitio
7.1 Sababu kubwa ya kawaida na Sababu kwa Kundi
Pata sababu kubwa ya kawaida ya maneno mawili au Zaidi
Katika mazoezi yafuatayo, pata sababu kubwa zaidi ya kawaida.
42, 60
- Jibu
-
6
450, 420
90, 150, 105
- Jibu
-
15
60, 294, 630
Sababu ya Sababu kuu ya kawaida kutoka kwa Polynomial
Katika mazoezi yafuatayo, fikiria sababu kubwa zaidi kutoka kwa kila polynomial.
\(24x−42\)
- Jibu
-
\(6(4x−7)\)
\(35y+84\)
\(15m^4+6m^{2}n\)
- Jibu
-
\(3m^2(5m2+2n)\)
\(24pt^4+16t^7\)
Kielelezo kwa Kundi
Katika mazoezi yafuatayo, sababu kwa kikundi.
\(ax−ay+bx−by\)
- Jibu
-
\((a+b)(x−y)\)
\(x^{2}y−xy^2+2x−2y\)
\(x^2+7x−3x−21\)
- Jibu
-
\((x−3)(x+7)\)
\(4x^2−16x+3x−12\)
\(m^3+m^2+m+1\)
- Jibu
-
\((m^2+1)(m+1)\)
\(5x−5y−y+x\)
7.2 Factor Trinomials ya fomu\(x^2+bx+c\)
Sababu Trinomials ya Fomu\(x^2+bx+c\)
Katika mazoezi yafuatayo, fanya kila trinomial ya fomu\(x^2+bx+c\)
\(u^2+17u+72\)
- Jibu
-
\((u+8)(u+9)\)
\(a^2+14a+33\)
\(k^2−16k+60\)
- Jibu
-
\((k−6)(k−10)\)
\(r^2−11r+28\)
\(y^2+6y−7\)
- Jibu
-
\((y+7)(y−1)\)
\(m^2+3m−54\)
\(s^2−2s−8\)
- Jibu
-
\((s−4)(s+2)\)
\(x^2−3x−10\)
Sababu Trinomials ya Fomu\(x^2+bxy+cy^2\)
Katika mifano ifuatayo, factor kila trinomial ya fomu\(x^2+bxy+cy^2\)
\(x^2+12xy+35y^2\)
- Jibu
-
\((x+5y)(x+7y)\)
\(u^2+14uv+48v^2\)
\(a^2+4ab−21b^2\)
- Jibu
-
\((a+7b)(a−3b)\)
\(p^2−5pq−36q^2\)
7.3 Kuzingatia Trinomials ya fomu\(ax^2+bx+c\)
Kutambua Mkakati wa awali kwa sababu Polynomials kabisa
Katika mazoezi yafuatayo, tambua njia bora ya kutumia ili kuzingatia kila polynomial.
\(y^2−17y+42\)
- Jibu
-
tengua FOIL
\(12r^2+32r+5\)
\(8a^3+72a\)
- Jibu
-
Sababu ya GCF
\(4m−mn−3n+12\)
Sababu Trinomials ya Fomu\(ax^2+bx+c\) with a GCF
Katika mazoezi yafuatayo, factor kabisa.
\(6x^2+42x+60\)
- Jibu
-
\(6(x+2)(x+5)\)
\(8a^2+32a+24\)
\(3n^4−12n^3−96n^2\)
- Jibu
-
\(3n^{2}(n−8)(n+4)\)
\(5y^4+25y^2−70y\)
Sababu Trinomials Kutumia Njia ya “ac”
Katika mazoezi yafuatayo, sababu.
\(2x^2+9x+4\)
- Jibu
-
\((x+4)(2x+1)\)
\(3y^2+17y+10\)
\(18a^2−9a+1\)
- Jibu
-
\((3a−1)(6a−1)\)
\(8u^2−14u+3\)
\(15p^2+2p−8\)
- Jibu
-
\((5p+4)(3p−2)\)
\(15x^2+6x−2\)
\(40s^2−s−6\)
- Jibu
-
\((5s−2)(8s+3)\)
\(20n^2−7n−3\)
Factor Trinomials na GCF Kutumia “ac” Njia
Katika mazoezi yafuatayo, sababu.
\(3x^2+3x−36\)
- Jibu
-
\(3(x+4)(x−3)\)
\(4x^2+4x−8\)
\(60y^2−85y−25\)
- Jibu
-
\(5(4y+1)(3y−5)\)
\(18a^2−57a−21\)
7.4 Factoring Maalum Bidhaa
Factor Perfect Square trinomials
Katika mazoezi yafuatayo, sababu.
\(25x^2+30x+9\)
- Jibu
-
\((5x+3)^2\)
\(16y^2+72y+81\)
\(36a^2−84ab+49b^2\)
- Jibu
-
\((6a−7b)^2\)
\(64r^2−176rs+121s^2\)
\(40x^2+360x+810\)
- Jibu
-
\(10(2x+9)^2\)
\(75u^2+180u+108\)
\(2y^3−16y^2+32y\)
- Jibu
-
\(2y(y−4)^2\)
\(5k^3−70k^2+245k\)
Katika mazoezi yafuatayo, sababu.
\(81r^2−25\)
- Jibu
-
\((9r−5)(9r+5)\)
\(49a^2−144\)
\(169m^2−n^2\)
- Jibu
-
\((13m+n)(13m−n)\)
\(64x^2−y^2\)
\(25p^2−1\)
- Jibu
-
\((5p−1)(5p+1)\)
\(1−16s^2\)
\(9−121y^2\)
- Jibu
-
\((3+11y)(3−11y)\)
\(100k^2−81\)
\(20x^2−125\)
- Jibu
-
\(5(2x−5)(2x+5)\)
\(18y^2−98\)
\(49u^3−9u\)
- Jibu
-
\(u(7u+3)(7u−3)\)
\(169n^3−n\)
Kiasi cha Kiasi na Tofauti za Cubes
Katika mazoezi yafuatayo, sababu.
\(a^3−125\)
- Jibu
-
\((a−5)(a^2+5a+25)\)
\(b^3−216\)
\(2m^3+54\)
- Jibu
-
\(2(m+3)(m^2−3m+9)\)
\(81x^3+3\)
Mkakati Mkuu wa 7.5 wa kuzingatia Polynomials
Kutambua na Tumia Njia sahihi ya Kufanya Kipolynomial Kikamilifu
Katika mazoezi yafuatayo, factor kabisa.
\(24x^3+44x^2\)
- Jibu
-
\(4x^{2}(6x+11)\)
\(24a^4−9a^3\)
\(16n^2−56mn+49m^2\)
- Jibu
-
\((4n−7m)^2\)
\(6a^2−25a−9\)
\(5r^2+22r−48\)
- Jibu
-
(r+6) (5r-8)
\(5u^4−45u^2\)
\(n^4−81\)
- Jibu
-
\((n^2+9)(n+3)(n−3)\)
\(64j^2+225\)
\(5x^2+5x−60\)
- Jibu
-
\(5(x−3)(x+4)\)
\(b^3−64\)
\(m^3+125\)
- Jibu
-
\((m+5)(m^2−5m+25)\)
\(2b^2−2bc+5cb−5c^2\)
7.6 Ulinganifu wa Quadratic
Tumia mali ya Bidhaa ya Zero
Katika mazoezi yafuatayo, tatua.
\((a−3)(a+7)=0\)
- Jibu
-
\(a=3\),\(a=−7\)
\((b−3)(b+10)=0\)
\(3m(2m−5)(m+6)=0\)
- Jibu
-
\(m=0\),\(m=−6\),\(m=\frac{5}{2}\)
\(7n(3n+8)(n−5)=0\)
Tatua Ulinganisho wa Quadratic kwa kuzingatia
Katika mazoezi yafuatayo, tatua.
\(x^2+9x+20=0\)
- Jibu
-
\(x=−4\),\(x=−5\)
\(y^2−y−72=0\)
\(2p^2−11p=40\)
- Jibu
-
\(p=−\frac{5}{2}\), p=8
\(q^3+3q^2+2q=0\)
\(144m^2−25=0\)
- Jibu
-
\(m=\frac{5}{12}\),\(m=−\frac{5}{12}\)
\(4n^2=36\)
Kutatua Maombi yanayotokana na equations Quadratic
Katika mazoezi yafuatayo, tatua.
Bidhaa ya namba mbili za mfululizo ni 462.
- Jibu
-
-21, -22
21, 22
Eneo la patio yenye umbo la mstatili 400 futi za mraba. Urefu wa patio ni futi 99 zaidi ya upana wake. Pata urefu na upana.
Mazoezi mtihani
Katika mazoezi yafuatayo, pata sababu kubwa ya kawaida katika kila kujieleza.
\(14y−42\)
- Jibu
-
\(7(y−6)\)
\(−6x^2−30x\)
\(80a^2+120a^3\)
- Jibu
-
\(40a^{2}(2+3a)\)
\(5m(m−1)+3(m−1)\)
Katika mazoezi yafuatayo, factor kabisa.
\(x^2+13x+36\)
- Jibu
-
\((x+7)(x+6)\)
\(p^2+pq−12q^2\)
\(3a^3−6a^2−72a\)
- Jibu
-
\(3a(a+4)(a-6)\)
\(s^2−25s+84\)
\(5n^2+30n+45\)
- Jibu
-
\(5(n+3)^2\)
\(64y^2−49\)
\(xy−8y+7x−56\)
- Jibu
-
\((x−8)(y+7)\)
\(40r^2+810\)
\(9s^2−12s+4\)
- Jibu
-
\((3s−2)^2\)
\(n^2+12n+36\)
\(100−a^2\)
- Jibu
-
\((10−a)(10+a)\)
\(6x^2−11x−10\)
\(3x^2−75y^2\)
- Jibu
-
\(3(x+5y)(x−5y)\)
\(c^3−1000d^3\)
\(ab−3b−2a+6\)
- Jibu
-
\((a−3)(b−2)\)
\(6u^2+3u−18\)
\(8m^2+22m+5\)
- Jibu
-
\((4m+1)(2m+5)\)
Katika mazoezi yafuatayo, tatua.
\(x^2+9x+20=0\)
\(y^2=y+132\)
- Jibu
-
\(y=−11\),\(y=12\)
\(5a^2+26a=24\)
\(9b^2−9=0\)
- Jibu
-
\(b=1\),\(b=−1\)
\(16−m^2=0\)
\(4n^2+19n+21=0\)
- Jibu
-
\(n=−\frac{7}{4}\), n=-3
\((x−3)(x+2)=6\)
Bidhaa ya integers mbili mfululizo ni 156.
- Jibu
-
12 na 13; -13 na -12
Eneo la kitanda cha mstatili ni inchi za mraba 168. Urefu wake ni urefu wa inchi mbili kuliko upana. Pata urefu na upana wa mahali pa mahali.