# Ontbinden in factoren (2)

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

1. $$80x^{4}-45x^{2}$$
2. $$12q^{11}+36q^{8}+27q^{5}$$
3. $$180q^{10}+420q^{7}s+245q^{4}s^2$$
4. $$216s^{11}-294s^{5}$$
5. $$2p^{5}-32p^{3}$$
6. $$24a^{11}-294a^{3}$$
7. $$-96q^{4}+294q^{2}$$
8. $$-72b^{7}+120b^{5}s-50b^{3}s^2$$
9. $$-y^{6}+64y^{4}$$
10. $$-50s^{6}-20s^{4}-2s^{2}$$
11. $$-5s^{6}-10s^{5}-5s^{4}$$
12. $$108y^{4}-180y^{3}+75y^{2}$$

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

##### Verbetersleutel

1. $$80x^{4}-45x^{2}=5x^{2}(16x^{2}-9)=5x^{2}(4x+3)(4x-3)$$
2. $$12q^{11}+36q^{8}+27q^{5}=3q^{5}(4q^{6}+12q^3+9)=3q^{5}(2q^3+3)^2$$
3. $$180q^{10}+420q^{7}s+245q^{4}s^2=5q^{4}(36q^{6}+84q^3s+49s^2)=5q^{4}(6q^3+7s)^2$$
4. $$216s^{11}-294s^{5}=6s^{5}(36s^{6}-49)=6s^{5}(6s^3+7)(6s^3-7)$$
5. $$2p^{5}-32p^{3}=2p^{3}(p^2-16)=2p^{3}(p+4)(p-4)$$
6. $$24a^{11}-294a^{3}=6a^{3}(4a^{8}-49)=6a^{3}(2a^4+7)(2a^4-7)$$
7. $$-96q^{4}+294q^{2}=-6q^{2}(16q^{2}-49)=-6q^{2}(4q+7)(4q-7)$$
8. $$-72b^{7}+120b^{5}s-50b^{3}s^2=-2b^{3}(36b^{4}-60b^2s+25s^2)=-2b^{3}(6b^2-5s)^2$$
9. $$-y^{6}+64y^{4}=-y^{4}(y^2-64)=-y^{4}(y+8)(y-8)$$
10. $$-50s^{6}-20s^{4}-2s^{2}=-2s^{2}(25s^{4}+10s^2+1)=-2s^{2}(5s^2+1)^2$$
11. $$-5s^{6}-10s^{5}-5s^{4}=-5s^{4}(s^2+2s+1)=-5s^{4}(s+1)^2$$
12. $$108y^{4}-180y^{3}+75y^{2}=3y^{2}(36y^{2}-60y+25)=3y^{2}(6y-5)^2$$
Oefeningengenerator vanhoeckes.be/wiskunde 2023-06-07 17:29:06