Question

t^3-2t^2-15t. Solve it by prime factorisation method and verify it. ​

Answer 1

${t}^{3} - 2 {t}^{2} - 15t = 0 \\ t( {t}^{2} - 2t - 15) = 0 \\ t = 0 \: \: or \: ({t}^{2} - 2t - 15) = 0 \\ t = 0 \: \: or \: ({t}^{2} - 5t + 3t - 15) = 0 \\ t = 0 \: \: or \: t(t - 5) + 3(t - 5) = 0 \\ t = 0 \: \: or \: (t + 3)(t - 5) = 0 \\ t = 0 \: \: or \: \: t = - 3 \: \: or \: \: t = 5$

now ,
》verification of t=0
0^3-2(0)^2-15(0)=0
the equation satisfies if t=0

》verification of t=-3
(-3)^3-2(-3)^2-15(-3)= -27-18+45=45-45=0
the equation satisfies if t=-3

》verification of t=5
5^3-2(5)^2-15(5) =125-50-75=125-125=0
the equation satisfies if t=5


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Answer 2

Answer:

t

3

−2t

2

−15t=0

t(t

2

−2t−15)=0

t=0or(t

2

−2t−15)=0

t=0or(t

2

−5t+3t−15)=0

t=0ort(t−5)+3(t−5)=0

t=0or(t+3)(t−5)=0

t=0ort=−3ort=5