Ontbinden in factoren (2)

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

1. \(-6y^{4}+6y^{2}\)
2. \(-p^{5}-2p^{4}-p^{3}\)
3. \(-2x^{6}+28x^{5}-98x^{4}\)
4. \(12b^{8}-147b^{2}\)
5. \(5s^{6}-320s^{4}\)
6. \(3b^{7}+42b^{6}+147b^{5}\)
7. \(50b^{6}+120b^{5}+72b^{4}\)
8. \(16p^{5}-p^{3}\)
9. \(18p^{4}-96p^{3}+128p^{2}\)
10. \(5q^{7}-45q^{5}\)
11. \(-125x^{4}+245x^{2}\)
12. \(-108p^{6}+180p^{5}-75p^{4}\)

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

Verbetersleutel

1. \(-6y^{4}+6y^{2}=-6y^{2}(y^2-1)=-6y^{2}(y-1)(y+1)\)
2. \(-p^{5}-2p^{4}-p^{3}=-p^{3}(p^2+2p+1)=-p^{3}(p+1)^2\)
3. \(-2x^{6}+28x^{5}-98x^{4}=-2x^{4}(x^2-14x+49)=-2x^{4}(x-7)^2\)
4. \(12b^{8}-147b^{2}=3b^{2}(4b^{6}-49)=3b^{2}(2b^3+7)(2b^3-7)\)
5. \(5s^{6}-320s^{4}=5s^{4}(s^2-64)=5s^{4}(s-8)(s+8)\)
6. \(3b^{7}+42b^{6}+147b^{5}=3b^{5}(b^2+14b+49)=3b^{5}(b+7)^2\)
7. \(50b^{6}+120b^{5}+72b^{4}=2b^{4}(25b^{2}+60b+36)=2b^{4}(5b+6)^2\)
8. \(16p^{5}-p^{3}=p^{3}(16p^{2}-1)=p^{3}(4p+1)(4p-1)\)
9. \(18p^{4}-96p^{3}+128p^{2}=2p^{2}(9p^{2}-48p+64)=2p^{2}(3p-8)^2\)
10. \(5q^{7}-45q^{5}=5q^{5}(q^2-9)=5q^{5}(q-3)(q+3)\)
11. \(-125x^{4}+245x^{2}=-5x^{2}(25x^{2}-49)=-5x^{2}(5x+7)(5x-7)\)
12. \(-108p^{6}+180p^{5}-75p^{4}=-3p^{4}(36p^{2}-60p+25)=-3p^{4}(6p-5)^2\)