Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. \(24x^{6}-294x^{4}\)
2. \(3x^{6}+6x^{5}+3x^{4}\)
3. \(-98a^{14}-140a^{9}-50a^{4}\)
4. \(-128s^{6}+224s^{4}x-98s^{2}x^2\)
5. \(96s^{15}-144s^{10}+54s^{5}\)
6. \(20p^{13}-245p^{3}\)
7. \(216s^{11}-294s^{3}\)
8. \(45b^{7}-5b^{3}\)
9. \(-5y^{7}+40y^{6}-80y^{5}\)
10. \(-192q^{13}+336q^{9}-147q^{5}\)
11. \(-16b^{18}+b^{4}\)
12. \(-6s^{7}+108s^{6}-486s^{5}\)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

1. \(24x^{6}-294x^{4}=6x^{4}(4x^{2}-49)=6x^{4}(2x+7)(2x-7)\)
2. \(3x^{6}+6x^{5}+3x^{4}=3x^{4}(x^2+2x+1)=3x^{4}(x+1)^2\)
3. \(-98a^{14}-140a^{9}-50a^{4}=-2a^{4}(49a^{10}+70a^5+25)=-2a^{4}(7a^5+5)^2\)
4. \(-128s^{6}+224s^{4}x-98s^{2}x^2=-2s^{2}(64s^{4}-112s^2x+49x^2)=-2s^{2}(8s^2-7x)^2\)
5. \(96s^{15}-144s^{10}+54s^{5}=6s^{5}(16s^{10}-24s^5+9)=6s^{5}(4s^5-3)^2\)
6. \(20p^{13}-245p^{3}=5p^{3}(4p^{10}-49)=5p^{3}(2p^5+7)(2p^5-7)\)
7. \(216s^{11}-294s^{3}=6s^{3}(36s^{8}-49)=6s^{3}(6s^4+7)(6s^4-7)\)
8. \(45b^{7}-5b^{3}=5b^{3}(9b^{4}-1)=5b^{3}(3b^2+1)(3b^2-1)\)
9. \(-5y^{7}+40y^{6}-80y^{5}=-5y^{5}(y^2-8y+16)=-5y^{5}(y-4)^2\)
10. \(-192q^{13}+336q^{9}-147q^{5}=-3q^{5}(64q^{8}-112q^4+49)=-3q^{5}(8q^4-7)^2\)
11. \(-16b^{18}+b^{4}=-b^{4}(16b^{14}-1)=-b^{4}(4b^7+1)(4b^7-1)\)
12. \(-6s^{7}+108s^{6}-486s^{5}=-6s^{5}(s^2-18s+81)=-6s^{5}(s-9)^2\)