How do I factor out a constant before factoring a quadratic?
Factor completely: \(3w^2 - 3w - 90\)
Answer (2)
3 w 2 − 3 w − 90 = 0 3 w 2 − w − 30 = 0 a = 1 , b = − 1 , c = − 30 Δ = b 2 − 4 a c = ( − 1 ) 2 − 4 ⋅ 1 ⋅ ( − 30 ) = 1 + 120 = 121 w 1 = 2 a − b − Δ = 2 1 − 121 = 2 1 − 11 = 2 − 10 = − 5
w 2 = 2 a − b + Δ = 2 1 + 121 = 2 1 + 11 = 2 12 = 6 A n s w er : w 2 − w − 30 = ( x + 5 ) ( x − 6 )
To factor the expression 3 w 2 − 3 w − 90 , we first factor out the common factor 3, resulting in 3 ( w 2 − w − 30 ) . Then, we factor the quadratic w 2 − w − 30 into ( w + 5 ) ( w − 6 ) . The final factored form is 3 ( w + 5 ) ( w − 6 ) .
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