Ontbinden in factoren (2)

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

1. \(-24a^{17}+150a^{5}\)
2. \(8x^{7}+8x^{6}+2x^{5}\)
3. \(-32s^{9}+48s^{7}-18s^{5}\)
4. \(8b^{9}+8b^{7}q+2b^{5}q^2\)
5. \(32q^{7}-2q^{3}\)
6. \(54s^{11}+144s^{7}x+96s^{3}x^2\)
7. \(-18y^{6}+8y^{4}\)
8. \(-180s^{6}+125s^{2}\)
9. \(-20p^{9}-60p^{6}-45p^{3}\)
10. \(108y^{12}-75y^{2}\)
11. \(6p^{6}-96p^{4}\)
12. \(3y^{7}-75y^{5}\)

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

Verbetersleutel

1. \(-24a^{17}+150a^{5}=-6a^{5}(4a^{12}-25)=-6a^{5}(2a^6+5)(2a^6-5)\)
2. \(8x^{7}+8x^{6}+2x^{5}=2x^{5}(4x^{2}+4x+1)=2x^{5}(2x+1)^2\)
3. \(-32s^{9}+48s^{7}-18s^{5}=-2s^{5}(16s^{4}-24s^2+9)=-2s^{5}(4s^2-3)^2\)
4. \(8b^{9}+8b^{7}q+2b^{5}q^2=2b^{5}(4b^{4}+4b^2q+q^2)=2b^{5}(2b^2+q)^2\)
5. \(32q^{7}-2q^{3}=2q^{3}(16q^{4}-1)=2q^{3}(4q^2+1)(4q^2-1)\)
6. \(54s^{11}+144s^{7}x+96s^{3}x^2=6s^{3}(9s^{8}+24s^4x+16x^2)=6s^{3}(3s^4+4x)^2\)
7. \(-18y^{6}+8y^{4}=-2y^{4}(9y^{2}-4)=-2y^{4}(3y+2)(3y-2)\)
8. \(-180s^{6}+125s^{2}=-5s^{2}(36s^{4}-25)=-5s^{2}(6s^2+5)(6s^2-5)\)
9. \(-20p^{9}-60p^{6}-45p^{3}=-5p^{3}(4p^{6}+12p^3+9)=-5p^{3}(2p^3+3)^2\)
10. \(108y^{12}-75y^{2}=3y^{2}(36y^{10}-25)=3y^{2}(6y^5+5)(6y^5-5)\)
11. \(6p^{6}-96p^{4}=6p^{4}(p^2-16)=6p^{4}(p+4)(p-4)\)
12. \(3y^{7}-75y^{5}=3y^{5}(y^2-25)=3y^{5}(y-5)(y+5)\)