Ontbinden in factoren (2)

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

1. \(-4a^{5}-28a^{4}-49a^{3}\)
2. \(-64q^{15}-80q^{10}-25q^{5}\)
3. \(-75x^{6}+12x^{4}\)
4. \(6a^{7}-96a^{6}+384a^{5}\)
5. \(-216b^{6}+6b^{4}\)
6. \(-18p^{13}+2p^{5}\)
7. \(128x^{7}+32x^{5}+2x^{3}\)
8. \(-98b^{8}-140b^{5}y-50b^{2}y^2\)
9. \(-72x^{5}+50x^{3}\)
10. \(-6y^{6}+294y^{4}\)
11. \(-80q^{9}+5q^{3}\)
12. \(64x^{8}-112x^{6}+49x^{4}\)

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

Verbetersleutel

1. \(-4a^{5}-28a^{4}-49a^{3}=-a^{3}(4a^{2}+28a+49)=-a^{3}(2a+7)^2\)
2. \(-64q^{15}-80q^{10}-25q^{5}=-q^{5}(64q^{10}+80q^5+25)=-q^{5}(8q^5+5)^2\)
3. \(-75x^{6}+12x^{4}=-3x^{4}(25x^{2}-4)=-3x^{4}(5x+2)(5x-2)\)
4. \(6a^{7}-96a^{6}+384a^{5}=6a^{5}(a^2-16a+64)=6a^{5}(a-8)^2\)
5. \(-216b^{6}+6b^{4}=-6b^{4}(36b^{2}-1)=-6b^{4}(6b+1)(6b-1)\)
6. \(-18p^{13}+2p^{5}=-2p^{5}(9p^{8}-1)=-2p^{5}(3p^4+1)(3p^4-1)\)
7. \(128x^{7}+32x^{5}+2x^{3}=2x^{3}(64x^{4}+16x^2+1)=2x^{3}(8x^2+1)^2\)
8. \(-98b^{8}-140b^{5}y-50b^{2}y^2=-2b^{2}(49b^{6}+70b^3y+25y^2)=-2b^{2}(7b^3+5y)^2\)
9. \(-72x^{5}+50x^{3}=-2x^{3}(36x^{2}-25)=-2x^{3}(6x+5)(6x-5)\)
10. \(-6y^{6}+294y^{4}=-6y^{4}(y^2-49)=-6y^{4}(y-7)(y+7)\)
11. \(-80q^{9}+5q^{3}=-5q^{3}(16q^{6}-1)=-5q^{3}(4q^3+1)(4q^3-1)\)
12. \(64x^{8}-112x^{6}+49x^{4}=x^{4}(64x^{4}-112x^2+49)=x^{4}(8x^2-7)^2\)