Ontbinden in factoren (2)

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

1. \(-80p^{17}+45p^{3}\)
2. \(320y^{5}-560y^{4}+245y^{3}\)
3. \(-6x^{7}+24x^{5}\)
4. \(180a^{7}-125a^{5}\)
5. \(5s^{5}+20s^{4}+20s^{3}\)
6. \(24b^{9}+72b^{6}+54b^{3}\)
7. \(-6s^{6}+384s^{4}\)
8. \(-12p^{7}-12p^{5}x-3p^{3}x^2\)
9. \(-80a^{11}+280a^{7}-245a^{3}\)
10. \(72p^{13}-2p^{5}\)
11. \(-147q^{4}+84q^{3}-12q^{2}\)
12. \(180s^{14}-300s^{9}y+125s^{4}y^2\)

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

Verbetersleutel

1. \(-80p^{17}+45p^{3}=-5p^{3}(16p^{14}-9)=-5p^{3}(4p^7+3)(4p^7-3)\)
2. \(320y^{5}-560y^{4}+245y^{3}=5y^{3}(64y^{2}-112y+49)=5y^{3}(8y-7)^2\)
3. \(-6x^{7}+24x^{5}=-6x^{5}(x^2-4)=-6x^{5}(x-2)(x+2)\)
4. \(180a^{7}-125a^{5}=5a^{5}(36a^{2}-25)=5a^{5}(6a+5)(6a-5)\)
5. \(5s^{5}+20s^{4}+20s^{3}=5s^{3}(s^2+4s+4)=5s^{3}(s+2)^2\)
6. \(24b^{9}+72b^{6}+54b^{3}=6b^{3}(4b^{6}+12b^3+9)=6b^{3}(2b^3+3)^2\)
7. \(-6s^{6}+384s^{4}=-6s^{4}(s^2-64)=-6s^{4}(s-8)(s+8)\)
8. \(-12p^{7}-12p^{5}x-3p^{3}x^2=-3p^{3}(4p^{4}+4p^2x+x^2)=-3p^{3}(2p^2+x)^2\)
9. \(-80a^{11}+280a^{7}-245a^{3}=-5a^{3}(16a^{8}-56a^4+49)=-5a^{3}(4a^4-7)^2\)
10. \(72p^{13}-2p^{5}=2p^{5}(36p^{8}-1)=2p^{5}(6p^4+1)(6p^4-1)\)
11. \(-147q^{4}+84q^{3}-12q^{2}=-3q^{2}(49q^{2}-28q+4)=-3q^{2}(7q-2)^2\)
12. \(180s^{14}-300s^{9}y+125s^{4}y^2=5s^{4}(36s^{10}-60s^5y+25y^2)=5s^{4}(6s^5-5y)^2\)