Ontbinden in factoren (2)

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

1. \(-48s^{6}+168s^{5}-147s^{4}\)
2. \(2x^{5}-50x^{3}\)
3. \(s^{5}+12s^{4}+36s^{3}\)
4. \(80b^{6}-280b^{5}+245b^{4}\)
5. \(3s^{5}-75s^{3}\)
6. \(-32p^{12}+112p^{7}y-98p^{2}y^2\)
7. \(3y^{4}+24y^{3}+48y^{2}\)
8. \(6q^{6}+60q^{5}+150q^{4}\)
9. \(125s^{21}-45s^{5}\)
10. \(-27q^{13}+90q^{9}x-75q^{5}x^2\)
11. \(5y^{5}-5y^{3}\)
12. \(98q^{4}+224q^{3}+128q^{2}\)

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

Verbetersleutel

1. \(-48s^{6}+168s^{5}-147s^{4}=-3s^{4}(16s^{2}-56s+49)=-3s^{4}(4s-7)^2\)
2. \(2x^{5}-50x^{3}=2x^{3}(x^2-25)=2x^{3}(x-5)(x+5)\)
3. \(s^{5}+12s^{4}+36s^{3}=s^{3}(s^2+12s+36)=s^{3}(s+6)^2\)
4. \(80b^{6}-280b^{5}+245b^{4}=5b^{4}(16b^{2}-56b+49)=5b^{4}(4b-7)^2\)
5. \(3s^{5}-75s^{3}=3s^{3}(s^2-25)=3s^{3}(s-5)(s+5)\)
6. \(-32p^{12}+112p^{7}y-98p^{2}y^2=-2p^{2}(16p^{10}-56p^5y+49y^2)=-2p^{2}(4p^5-7y)^2\)
7. \(3y^{4}+24y^{3}+48y^{2}=3y^{2}(y^2+8y+16)=3y^{2}(y+4)^2\)
8. \(6q^{6}+60q^{5}+150q^{4}=6q^{4}(q^2+10q+25)=6q^{4}(q+5)^2\)
9. \(125s^{21}-45s^{5}=5s^{5}(25s^{16}-9)=5s^{5}(5s^8+3)(5s^8-3)\)
10. \(-27q^{13}+90q^{9}x-75q^{5}x^2=-3q^{5}(9q^{8}-30q^4x+25x^2)=-3q^{5}(3q^4-5x)^2\)
11. \(5y^{5}-5y^{3}=5y^{3}(y^2-1)=5y^{3}(y-1)(y+1)\)
12. \(98q^{4}+224q^{3}+128q^{2}=2q^{2}(49q^{2}+112q+64)=2q^{2}(7q+8)^2\)