Ontbinden in factoren (2)

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

1. \(-150a^{6}-360a^{5}-216a^{4}\)
2. \(-180s^{16}+245s^{2}\)
3. \(16p^{4}+24p^{3}+9p^{2}\)
4. \(-6x^{4}+150x^{2}\)
5. \(5p^{5}-5p^{3}\)
6. \(-x^{5}+16x^{3}\)
7. \(-48a^{9}+168a^{7}-147a^{5}\)
8. \(-125y^{4}-50y^{3}-5y^{2}\)
9. \(-x^{7}+36x^{5}\)
10. \(8q^{15}-18q^{3}\)
11. \(384b^{10}-672b^{7}x+294b^{4}x^2\)
12. \(-4q^{6}+25q^{4}\)

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

Verbetersleutel

1. \(-150a^{6}-360a^{5}-216a^{4}=-6a^{4}(25a^{2}+60a+36)=-6a^{4}(5a+6)^2\)
2. \(-180s^{16}+245s^{2}=-5s^{2}(36s^{14}-49)=-5s^{2}(6s^7+7)(6s^7-7)\)
3. \(16p^{4}+24p^{3}+9p^{2}=p^{2}(16p^{2}+24p+9)=p^{2}(4p+3)^2\)
4. \(-6x^{4}+150x^{2}=-6x^{2}(x^2-25)=-6x^{2}(x+5)(x-5)\)
5. \(5p^{5}-5p^{3}=5p^{3}(p^2-1)=5p^{3}(p+1)(p-1)\)
6. \(-x^{5}+16x^{3}=-x^{3}(x^2-16)=-x^{3}(x+4)(x-4)\)
7. \(-48a^{9}+168a^{7}-147a^{5}=-3a^{5}(16a^{4}-56a^2+49)=-3a^{5}(4a^2-7)^2\)
8. \(-125y^{4}-50y^{3}-5y^{2}=-5y^{2}(25y^{2}+10y+1)=-5y^{2}(5y+1)^2\)
9. \(-x^{7}+36x^{5}=-x^{5}(x^2-36)=-x^{5}(x-6)(x+6)\)
10. \(8q^{15}-18q^{3}=2q^{3}(4q^{12}-9)=2q^{3}(2q^6+3)(2q^6-3)\)
11. \(384b^{10}-672b^{7}x+294b^{4}x^2=6b^{4}(64b^{6}-112b^3x+49x^2)=6b^{4}(8b^3-7x)^2\)
12. \(-4q^{6}+25q^{4}=-q^{4}(4q^{2}-25)=-q^{4}(2q+5)(2q-5)\)