write the expression in factored form

2. ) n 2 − 9 n + 14 = 0 a = 1 , b = − 9 , c = 14 Δ = b 2 − 4 a c = ( − 9 ) 2 − 4 ⋅ 1 ⋅ 14 = 81 − 56 = 25 1 ​ = 2 a − b − Δ ​ ​ = 2 9 − 25 ​ ​ = 2 9 − 5 ​ = 2 4 ​ = 2
n 2 ​ = 2 a − b + Δ ​ ​ = 2 9 + 25 ​ ​ = 2 9 + 5 ​ = 2 14 ​ = 7 A n s w er : n 2 − 9 n + 14 = ( n − 2 ) ( n − 7 )
3. ) n 2 + 4 n − 12 = 0 a = 1 , b = 4 , c = − 12 Δ = b 2 − 4 a c = 4 2 − 4 ⋅ 1 ⋅ ( − 12 ) = 16 + 48 = 64 1 ​ = 2 a − b − Δ ​ ​ = 2 − 4 − 64 ​ ​ = 2 − 4 − 8 ​ = 2 − 12 ​ = − 6
n 2 ​ = 2 a − b + Δ ​ ​ = 2 − 4 + 64 ​ ​ = 2 − 4 + 8 ​ = 2 4 ​ = 2 A n s w er : n 2 + 4 n − 12 = ( n + 6 ) ( n − 2 )
second way :
2. ) n 2 − 9 n + 14 = n 2 − 9 n + 2 n − 2 n + 14 = n 2 − 7 x − 2 n + 14 = = n ( n − 7 ) − 2 ( n − 7 ) = ( n − 7 ) ( n − 2 ) A n s w er : n 2 − 9 n + 14 = ( n − 2 ) ( n − 7 )
3. ) n 2 + 4 n − 12 = n 2 + 4 n + 2 n − 2 n − 12 = n 2 + 6 n − 2 n − 12 = = n ( n + 6 ) − 2 ( n + 6 ) = ( n + 6 ) ( n − 2 ) A n s w er : n 2 + 4 n − 12 = ( n + 6 ) ( n − 2 )

Answered by Lilith | 2024-06-10

n^2-9n +14 n^2-7n-2n+14 n(n-7) -2(n-7) (n-2)(n-7)

Answered by missyslone | 2024-06-10

The expression n 2 − 9 n + 14 can be factored into ( n − 2 ) ( n − 7 ) . This is found using the quadratic formula to determine the roots of the equation. The roots are 2 and 7, allowing us to express the quadratic in its factored form.
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Answered by Lilith | 2025-02-13