Question

factorize 9z³-27z²-100z+300,if it is given that (3z+10)is a factor of it

Answer 1

9z³ - 27z² - 100z + 300
= 9z³ + 30z² - 57z² - 190z + 90z + 300
= 3z²(3z + 10) - 19z(3z + 10) + 30(3z + 10)
= (3z + 10)(3z² - 19z + 30)
= (3z + 10)[3z² - 10z - 9z + 30]
= (3z + 10)[z(3z + 10) -3(3z + 10)]
= (3z + 10)(3z + 10)(z - 3)

Hence, factorisation of 9z³ - 27z² - 100z + 300 = (3z + 10)(3z + 10)(z - 3)