Ontbinden in factoren (2)

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

1. \(-150s^{4}-240s^{3}-96s^{2}\)
2. \(20s^{5}-45s^{3}\)
3. \(50a^{15}-32a^{3}\)
4. \(-48x^{4}+75x^{2}\)
5. \(-9a^{15}+25a^{5}\)
6. \(3q^{7}-54q^{6}+243q^{5}\)
7. \(180b^{5}-300b^{4}+125b^{3}\)
8. \(-27x^{5}+147x^{3}\)
9. \(-6x^{4}+150x^{2}\)
10. \(48s^{4}-27s^{2}\)
11. \(-72a^{7}-120a^{5}x-50a^{3}x^2\)
12. \(-6b^{5}-24b^{4}-24b^{3}\)

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

Verbetersleutel

1. \(-150s^{4}-240s^{3}-96s^{2}=-6s^{2}(25s^{2}+40s+16)=-6s^{2}(5s+4)^2\)
2. \(20s^{5}-45s^{3}=5s^{3}(4s^{2}-9)=5s^{3}(2s+3)(2s-3)\)
3. \(50a^{15}-32a^{3}=2a^{3}(25a^{12}-16)=2a^{3}(5a^6+4)(5a^6-4)\)
4. \(-48x^{4}+75x^{2}=-3x^{2}(16x^{2}-25)=-3x^{2}(4x+5)(4x-5)\)
5. \(-9a^{15}+25a^{5}=-a^{5}(9a^{10}-25)=-a^{5}(3a^5+5)(3a^5-5)\)
6. \(3q^{7}-54q^{6}+243q^{5}=3q^{5}(q^2-18q+81)=3q^{5}(q-9)^2\)
7. \(180b^{5}-300b^{4}+125b^{3}=5b^{3}(36b^{2}-60b+25)=5b^{3}(6b-5)^2\)
8. \(-27x^{5}+147x^{3}=-3x^{3}(9x^{2}-49)=-3x^{3}(3x+7)(3x-7)\)
9. \(-6x^{4}+150x^{2}=-6x^{2}(x^2-25)=-6x^{2}(x-5)(x+5)\)
10. \(48s^{4}-27s^{2}=3s^{2}(16s^{2}-9)=3s^{2}(4s+3)(4s-3)\)
11. \(-72a^{7}-120a^{5}x-50a^{3}x^2=-2a^{3}(36a^{4}+60a^2x+25x^2)=-2a^{3}(6a^2+5x)^2\)
12. \(-6b^{5}-24b^{4}-24b^{3}=-6b^{3}(b^2+4b+4)=-6b^{3}(b+2)^2\)