Ontbinden in factoren (2)

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

1. \(x^{7}+2x^{6}+x^{5}\)
2. \(3x^{4}+48x^{3}+192x^{2}\)
3. \(18a^{10}+48a^{6}p+32a^{2}p^2\)
4. \(216p^{10}-360p^{6}+150p^{2}\)
5. \(6x^{4}-24x^{2}\)
6. \(-50y^{15}+80y^{10}-32y^{5}\)
7. \(-6b^{4}+6b^{2}\)
8. \(-32p^{7}-16p^{6}-2p^{5}\)
9. \(12q^{13}+36q^{8}+27q^{3}\)
10. \(216y^{7}+72y^{6}+6y^{5}\)
11. \(2y^{6}-36y^{5}+162y^{4}\)
12. \(108b^{7}-180b^{6}+75b^{5}\)

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

Verbetersleutel

1. \(x^{7}+2x^{6}+x^{5}=x^{5}(x^2+2x+1)=x^{5}(x+1)^2\)
2. \(3x^{4}+48x^{3}+192x^{2}=3x^{2}(x^2+16x+64)=3x^{2}(x+8)^2\)
3. \(18a^{10}+48a^{6}p+32a^{2}p^2=2a^{2}(9a^{8}+24a^4p+16p^2)=2a^{2}(3a^4+4p)^2\)
4. \(216p^{10}-360p^{6}+150p^{2}=6p^{2}(36p^{8}-60p^4+25)=6p^{2}(6p^4-5)^2\)
5. \(6x^{4}-24x^{2}=6x^{2}(x^2-4)=6x^{2}(x+2)(x-2)\)
6. \(-50y^{15}+80y^{10}-32y^{5}=-2y^{5}(25y^{10}-40y^5+16)=-2y^{5}(5y^5-4)^2\)
7. \(-6b^{4}+6b^{2}=-6b^{2}(b^2-1)=-6b^{2}(b+1)(b-1)\)
8. \(-32p^{7}-16p^{6}-2p^{5}=-2p^{5}(16p^{2}+8p+1)=-2p^{5}(4p+1)^2\)
9. \(12q^{13}+36q^{8}+27q^{3}=3q^{3}(4q^{10}+12q^5+9)=3q^{3}(2q^5+3)^2\)
10. \(216y^{7}+72y^{6}+6y^{5}=6y^{5}(36y^{2}+12y+1)=6y^{5}(6y+1)^2\)
11. \(2y^{6}-36y^{5}+162y^{4}=2y^{4}(y^2-18y+81)=2y^{4}(y-9)^2\)
12. \(108b^{7}-180b^{6}+75b^{5}=3b^{5}(36b^{2}-60b+25)=3b^{5}(6b-5)^2\)