Ontbinden in factoren (2)

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

1. \(-216q^{7}+360q^{6}-150q^{5}\)
2. \(-5x^{6}+80x^{4}\)
3. \(3x^{5}-108x^{3}\)
4. \(-2s^{6}+36s^{5}-162s^{4}\)
5. \(-2x^{7}+128x^{5}\)
6. \(125a^{14}-5a^{4}\)
7. \(-2p^{4}+32p^{2}\)
8. \(-9y^{8}+y^{2}\)
9. \(128b^{13}+96b^{8}y+18b^{3}y^2\)
10. \(8q^{13}+8q^{9}+2q^{5}\)
11. \(-75b^{14}+108b^{2}\)
12. \(-6y^{5}-48y^{4}-96y^{3}\)

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

Verbetersleutel

1. \(-216q^{7}+360q^{6}-150q^{5}=-6q^{5}(36q^{2}-60q+25)=-6q^{5}(6q-5)^2\)
2. \(-5x^{6}+80x^{4}=-5x^{4}(x^2-16)=-5x^{4}(x-4)(x+4)\)
3. \(3x^{5}-108x^{3}=3x^{3}(x^2-36)=3x^{3}(x-6)(x+6)\)
4. \(-2s^{6}+36s^{5}-162s^{4}=-2s^{4}(s^2-18s+81)=-2s^{4}(s-9)^2\)
5. \(-2x^{7}+128x^{5}=-2x^{5}(x^2-64)=-2x^{5}(x-8)(x+8)\)
6. \(125a^{14}-5a^{4}=5a^{4}(25a^{10}-1)=5a^{4}(5a^5+1)(5a^5-1)\)
7. \(-2p^{4}+32p^{2}=-2p^{2}(p^2-16)=-2p^{2}(p+4)(p-4)\)
8. \(-9y^{8}+y^{2}=-y^{2}(9y^{6}-1)=-y^{2}(3y^3+1)(3y^3-1)\)
9. \(128b^{13}+96b^{8}y+18b^{3}y^2=2b^{3}(64b^{10}+48b^5y+9y^2)=2b^{3}(8b^5+3y)^2\)
10. \(8q^{13}+8q^{9}+2q^{5}=2q^{5}(4q^{8}+4q^4+1)=2q^{5}(2q^4+1)^2\)
11. \(-75b^{14}+108b^{2}=-3b^{2}(25b^{12}-36)=-3b^{2}(5b^6+6)(5b^6-6)\)
12. \(-6y^{5}-48y^{4}-96y^{3}=-6y^{3}(y^2+8y+16)=-6y^{3}(y+4)^2\)