Ontbinden in factoren (2)

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

1. \(49p^{7}-42p^{6}+9p^{5}\)
2. \(-45a^{4}+80a^{2}\)
3. \(-32s^{5}+48s^{4}-18s^{3}\)
4. \(-128q^{10}-96q^{6}s-18q^{2}s^2\)
5. \(-36s^{6}+25s^{4}\)
6. \(6a^{6}-294a^{4}\)
7. \(20p^{11}+100p^{7}q+125p^{3}q^2\)
8. \(4q^{6}-25q^{4}\)
9. \(-320q^{7}-80q^{5}-5q^{3}\)
10. \(-54b^{14}+180b^{9}x-150b^{4}x^2\)
11. \(-9q^{10}+49q^{4}\)
12. \(150q^{16}-6q^{4}\)

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

Verbetersleutel

1. \(49p^{7}-42p^{6}+9p^{5}=p^{5}(49p^{2}-42p+9)=p^{5}(7p-3)^2\)
2. \(-45a^{4}+80a^{2}=-5a^{2}(9a^{2}-16)=-5a^{2}(3a+4)(3a-4)\)
3. \(-32s^{5}+48s^{4}-18s^{3}=-2s^{3}(16s^{2}-24s+9)=-2s^{3}(4s-3)^2\)
4. \(-128q^{10}-96q^{6}s-18q^{2}s^2=-2q^{2}(64q^{8}+48q^4s+9s^2)=-2q^{2}(8q^4+3s)^2\)
5. \(-36s^{6}+25s^{4}=-s^{4}(36s^{2}-25)=-s^{4}(6s+5)(6s-5)\)
6. \(6a^{6}-294a^{4}=6a^{4}(a^2-49)=6a^{4}(a-7)(a+7)\)
7. \(20p^{11}+100p^{7}q+125p^{3}q^2=5p^{3}(4p^{8}+20p^4q+25q^2)=5p^{3}(2p^4+5q)^2\)
8. \(4q^{6}-25q^{4}=q^{4}(4q^{2}-25)=q^{4}(2q+5)(2q-5)\)
9. \(-320q^{7}-80q^{5}-5q^{3}=-5q^{3}(64q^{4}+16q^2+1)=-5q^{3}(8q^2+1)^2\)
10. \(-54b^{14}+180b^{9}x-150b^{4}x^2=-6b^{4}(9b^{10}-30b^5x+25x^2)=-6b^{4}(3b^5-5x)^2\)
11. \(-9q^{10}+49q^{4}=-q^{4}(9q^{6}-49)=-q^{4}(3q^3+7)(3q^3-7)\)
12. \(150q^{16}-6q^{4}=6q^{4}(25q^{12}-1)=6q^{4}(5q^6+1)(5q^6-1)\)