Ontbinden in factoren (2)

Hoofdmenu Eentje per keer  🖨

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

1. \(-6x^{5}+294x^{3}\)
2. \(-20s^{21}+245s^{5}\)
3. \(-5y^{4}+20y^{2}\)
4. \(-45x^{5}-240x^{4}-320x^{3}\)
5. \(150p^{10}+360p^{6}y+216p^{2}y^2\)
6. \(108p^{9}+180p^{7}y+75p^{5}y^2\)
7. \(s^{5}-18s^{4}+81s^{3}\)
8. \(18b^{5}-98b^{3}\)
9. \(4y^{11}+4y^{7}+y^{3}\)
10. \(180x^{6}+60x^{5}+5x^{4}\)
11. \(-25s^{12}-10s^{8}y-s^{4}y^2\)
12. \(-50q^{7}+32q^{5}\)

---

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

Verbetersleutel

1. \(-6x^{5}+294x^{3}=-6x^{3}(x^2-49)=-6x^{3}(x-7)(x+7)\)
2. \(-20s^{21}+245s^{5}=-5s^{5}(4s^{16}-49)=-5s^{5}(2s^8+7)(2s^8-7)\)
3. \(-5y^{4}+20y^{2}=-5y^{2}(y^2-4)=-5y^{2}(y+2)(y-2)\)
4. \(-45x^{5}-240x^{4}-320x^{3}=-5x^{3}(9x^{2}+48x+64)=-5x^{3}(3x+8)^2\)
5. \(150p^{10}+360p^{6}y+216p^{2}y^2=6p^{2}(25p^{8}+60p^4y+36y^2)=6p^{2}(5p^4+6y)^2\)
6. \(108p^{9}+180p^{7}y+75p^{5}y^2=3p^{5}(36p^{4}+60p^2y+25y^2)=3p^{5}(6p^2+5y)^2\)
7. \(s^{5}-18s^{4}+81s^{3}=s^{3}(s^2-18s+81)=s^{3}(s-9)^2\)
8. \(18b^{5}-98b^{3}=2b^{3}(9b^{2}-49)=2b^{3}(3b+7)(3b-7)\)
9. \(4y^{11}+4y^{7}+y^{3}=y^{3}(4y^{8}+4y^4+1)=y^{3}(2y^4+1)^2\)
10. \(180x^{6}+60x^{5}+5x^{4}=5x^{4}(36x^{2}+12x+1)=5x^{4}(6x+1)^2\)
11. \(-25s^{12}-10s^{8}y-s^{4}y^2=-s^{4}(25s^{8}+10s^4y+y^2)=-s^{4}(5s^4+y)^2\)
12. \(-50q^{7}+32q^{5}=-2q^{5}(25q^{2}-16)=-2q^{5}(5q+4)(5q-4)\)