What is \(2t^3 + 8t^2 - 24t\) in factored form?
Answer (3)
2 t 3 + 8 t 2 − 24 t = 0 2 t ( t 2 + 4 t − 12 ) = 0 2 t = 0 ∨ t 2 + 4 t − 12 = 0
t 2 + 4 t − 12 = 0 a = 1 ; b = 4 ; c = − 12 Δ = b 2 − 4 a c Δ = 4 2 − 4 ⋅ 1 ⋅ ( − 12 ) = 16 + 48 = 64 Δ = 64
t 1 = 2 a − b − Δ ∨ t 2 = 2 a − b + Δ t 1 = 2 ⋅ 1 − 4 − 8 ∨ t 2 = 2 ⋅ 1 − 4 + 8 t 1 = 2 − 12 ∨ t 2 = 2 4 t 1 = − 6 ∨ t 2 = 2
2 t ( t 2 + 4 t − 12 ) = 0 2 t ( t + 6 ) ( t − 2 ) = 0
2t (t-2) (t+6) ;
The expression 2 t 3 + 8 t 2 − 24 t can be factored as 2 t ( t + 6 ) ( t − 2 ) . To do this, we first factored out the GCF, which is 2 t , and then factored the quadratic t 2 + 4 t − 12 into ( t + 6 ) ( t − 2 ) .
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