Ontbinden in factoren (2)

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

1. \(36q^{4}+60q^{3}+25q^{2}\)
2. \(-27p^{9}+90p^{6}q-75p^{3}q^2\)
3. \(2x^{5}-16x^{4}+32x^{3}\)
4. \(-36p^{12}-60p^{7}s-25p^{2}s^2\)
5. \(192p^{5}+48p^{4}+3p^{3}\)
6. \(x^{4}+14x^{3}+49x^{2}\)
7. \(-3y^{7}+147y^{5}\)
8. \(245q^{10}-420q^{6}+180q^{2}\)
9. \(-180a^{14}+300a^{9}-125a^{4}\)
10. \(27x^{19}-147x^{5}\)
11. \(-5q^{4}-60q^{3}-180q^{2}\)
12. \(216p^{13}-6p^{3}\)

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

Verbetersleutel

1. \(36q^{4}+60q^{3}+25q^{2}=q^{2}(36q^{2}+60q+25)=q^{2}(6q+5)^2\)
2. \(-27p^{9}+90p^{6}q-75p^{3}q^2=-3p^{3}(9p^{6}-30p^3q+25q^2)=-3p^{3}(3p^3-5q)^2\)
3. \(2x^{5}-16x^{4}+32x^{3}=2x^{3}(x^2-8x+16)=2x^{3}(x-4)^2\)
4. \(-36p^{12}-60p^{7}s-25p^{2}s^2=-p^{2}(36p^{10}+60p^5s+25s^2)=-p^{2}(6p^5+5s)^2\)
5. \(192p^{5}+48p^{4}+3p^{3}=3p^{3}(64p^{2}+16p+1)=3p^{3}(8p+1)^2\)
6. \(x^{4}+14x^{3}+49x^{2}=x^{2}(x^2+14x+49)=x^{2}(x+7)^2\)
7. \(-3y^{7}+147y^{5}=-3y^{5}(y^2-49)=-3y^{5}(y-7)(y+7)\)
8. \(245q^{10}-420q^{6}+180q^{2}=5q^{2}(49q^{8}-84q^4+36)=5q^{2}(7q^4-6)^2\)
9. \(-180a^{14}+300a^{9}-125a^{4}=-5a^{4}(36a^{10}-60a^5+25)=-5a^{4}(6a^5-5)^2\)
10. \(27x^{19}-147x^{5}=3x^{5}(9x^{14}-49)=3x^{5}(3x^7+7)(3x^7-7)\)
11. \(-5q^{4}-60q^{3}-180q^{2}=-5q^{2}(q^2+12q+36)=-5q^{2}(q+6)^2\)
12. \(216p^{13}-6p^{3}=6p^{3}(36p^{10}-1)=6p^{3}(6p^5+1)(6p^5-1)\)