Ontbinden in factoren (2)

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

1. \(-384s^{6}-96s^{5}-6s^{4}\)
2. \(-150p^{14}+240p^{9}s-96p^{4}s^2\)
3. \(-320y^{10}-80y^{6}-5y^{2}\)
4. \(-27b^{12}+90b^{8}s-75b^{4}s^2\)
5. \(49p^{4}+84p^{3}+36p^{2}\)
6. \(50a^{13}-140a^{9}x+98a^{5}x^2\)
7. \(45y^{7}-80y^{5}\)
8. \(-4x^{8}+49x^{2}\)
9. \(96b^{6}+48b^{4}x+6b^{2}x^2\)
10. \(-80q^{10}+245q^{2}\)
11. \(2b^{4}-2b^{2}\)
12. \(-6p^{7}-36p^{6}-54p^{5}\)

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

Verbetersleutel

1. \(-384s^{6}-96s^{5}-6s^{4}=-6s^{4}(64s^{2}+16s+1)=-6s^{4}(8s+1)^2\)
2. \(-150p^{14}+240p^{9}s-96p^{4}s^2=-6p^{4}(25p^{10}-40p^5s+16s^2)=-6p^{4}(5p^5-4s)^2\)
3. \(-320y^{10}-80y^{6}-5y^{2}=-5y^{2}(64y^{8}+16y^4+1)=-5y^{2}(8y^4+1)^2\)
4. \(-27b^{12}+90b^{8}s-75b^{4}s^2=-3b^{4}(9b^{8}-30b^4s+25s^2)=-3b^{4}(3b^4-5s)^2\)
5. \(49p^{4}+84p^{3}+36p^{2}=p^{2}(49p^{2}+84p+36)=p^{2}(7p+6)^2\)
6. \(50a^{13}-140a^{9}x+98a^{5}x^2=2a^{5}(25a^{8}-70a^4x+49x^2)=2a^{5}(5a^4-7x)^2\)
7. \(45y^{7}-80y^{5}=5y^{5}(9y^{2}-16)=5y^{5}(3y+4)(3y-4)\)
8. \(-4x^{8}+49x^{2}=-x^{2}(4x^{6}-49)=-x^{2}(2x^3+7)(2x^3-7)\)
9. \(96b^{6}+48b^{4}x+6b^{2}x^2=6b^{2}(16b^{4}+8b^2x+x^2)=6b^{2}(4b^2+x)^2\)
10. \(-80q^{10}+245q^{2}=-5q^{2}(16q^{8}-49)=-5q^{2}(4q^4+7)(4q^4-7)\)
11. \(2b^{4}-2b^{2}=2b^{2}(b^2-1)=2b^{2}(b-1)(b+1)\)
12. \(-6p^{7}-36p^{6}-54p^{5}=-6p^{5}(p^2+6p+9)=-6p^{5}(p+3)^2\)