How to factor completely: \(15x^2 - 40x - 15\)

15 x 2 − 40 x − 15 = 0 / : 5 3 x 2 − 8 x − 3 = 0 a = 3 , b = − 8 , c = − 3 Δ = b 2 − 4 a c = ( − 8 ) 2 − 4 ⋅ 3 ⋅ ( − 3 ) = 64 + 36 = 100 x 1 ​ = 2 a − b − Δ ​ = 2 ⋅ 3 8 − 100 ​ ​ = 6 8 − 10 ​ = − 6 2 ​ = − 3 1 ​
x 2 ​ = 2 a − b + Δ ​ = 2 ⋅ 3 8 + 100 ​ ​ = 6 8 + 10 ​ = 6 18 ​ = 3 3 x 2 − 8 x − 3 = 3 ( x + 3 1 ​ ) ( x − 3 ) = ( 3 x + 1 ) ( x − 3 ) A n s w er : 15 x 2 − 40 x − 15 = 3 x 2 − 8 x − 3 = ( 3 x + 1 ) ( x − 3 )

Answered by Lilith | 2024-06-10

To factor 15 x 2 − 40 x − 15 , first factor out the GCF which is 5 , yielding 5 ( 3 x 2 − 8 x − 3 ) . Then, factor the quadratic expression to obtain the complete factorization as 5 ( 3 x + 1 ) ( x − 3 ) .
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Answered by Lilith | 2024-12-24