Ontbinden in factoren (2)

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

1. \(-24p^{7}+294p^{3}\)
2. \(2p^{7}+12p^{6}+18p^{5}\)
3. \(-20a^{10}-20a^{6}q-5a^{2}q^2\)
4. \(-48y^{9}-72y^{7}-27y^{5}\)
5. \(-150x^{4}-240x^{3}-96x^{2}\)
6. \(6q^{7}-108q^{6}+486q^{5}\)
7. \(-128y^{9}+224y^{6}-98y^{3}\)
8. \(4b^{17}-9b^{5}\)
9. \(108a^{9}+180a^{7}+75a^{5}\)
10. \(48x^{13}-27x^{3}\)
11. \(-5b^{7}-60b^{6}-180b^{5}\)
12. \(8p^{13}-18p^{5}\)

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

Verbetersleutel

1. \(-24p^{7}+294p^{3}=-6p^{3}(4p^{4}-49)=-6p^{3}(2p^2+7)(2p^2-7)\)
2. \(2p^{7}+12p^{6}+18p^{5}=2p^{5}(p^2+6p+9)=2p^{5}(p+3)^2\)
3. \(-20a^{10}-20a^{6}q-5a^{2}q^2=-5a^{2}(4a^{8}+4a^4q+q^2)=-5a^{2}(2a^4+q)^2\)
4. \(-48y^{9}-72y^{7}-27y^{5}=-3y^{5}(16y^{4}+24y^2+9)=-3y^{5}(4y^2+3)^2\)
5. \(-150x^{4}-240x^{3}-96x^{2}=-6x^{2}(25x^{2}+40x+16)=-6x^{2}(5x+4)^2\)
6. \(6q^{7}-108q^{6}+486q^{5}=6q^{5}(q^2-18q+81)=6q^{5}(q-9)^2\)
7. \(-128y^{9}+224y^{6}-98y^{3}=-2y^{3}(64y^{6}-112y^3+49)=-2y^{3}(8y^3-7)^2\)
8. \(4b^{17}-9b^{5}=b^{5}(4b^{12}-9)=b^{5}(2b^6+3)(2b^6-3)\)
9. \(108a^{9}+180a^{7}+75a^{5}=3a^{5}(36a^{4}+60a^2+25)=3a^{5}(6a^2+5)^2\)
10. \(48x^{13}-27x^{3}=3x^{3}(16x^{10}-9)=3x^{3}(4x^5+3)(4x^5-3)\)
11. \(-5b^{7}-60b^{6}-180b^{5}=-5b^{5}(b^2+12b+36)=-5b^{5}(b+6)^2\)
12. \(8p^{13}-18p^{5}=2p^{5}(4p^{8}-9)=2p^{5}(2p^4+3)(2p^4-3)\)