Question

Write the expression in factored form

Answer 1

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

Answer 2

`2.)\\ \\ n^2 - 9n +14 = 0 \\ \\ a=1 , \ b = -9, \ c = 14 \\ \\\Delta =b^2-4ac = (-9)^2 -4\cdot1\cdot 14 = 81 -56 = 25 \\ \\n_(1)=(-b-√(\Delta) )/(2a)=(9-√(25))/(2 )=( 9-5)/(2)=(4)/(2)= 2`


`n_(2)=(-b+√(\Delta) )/(2a)=(9+√(25))/(2 )=( 9+5)/(2)=(14)/(2)= 7 \\ \\ Answer : \ n^2 - 9n +14 =(n-2)(n-7)`




`3.)\\ \\ n^2 + 4n - 12 =0 \\ \\ a=1 , \ b = 4, \ c = -12 \\ \\\Delta =b^2-4ac = 4^2 -4\cdot1\cdot (-12) = 16+48=64 \\ \\n_(1)=(-b-√(\Delta) )/(2a)=(-4-√(64))/(2 )=( -4-8)/(2)=(-12)/(2)= -6`


`n_(2)=(-b+√(\Delta) )/(2a)= (-4+√(64))/(2 )=( -4+8)/(2)=(4)/(2)=2\\ \\ Answer : \ n^2 +4n -12 =(n+6)(n-2)`


second way :


`2.)\\ \\ n^2 - 9n +14 = n^2 - 9n+2n -2n +14 = n^2 - 7x -2n +14 =\\ \\ = n(n-7)-2(n-7)=(n-7)(n- 2)\\ \\ \\ Answer : \ n^2 - 9n +14 =(n-2)(n-7)`



`3.)\\ \\ n^2 + 4n - 12 = n^2 + 4n +2n - 2n - 12 = n^2 + 6n - 2n - 12 =\\ \\ = n(n+6) -2(n+6)=(n+6)(n-2) \\ \\ \\ Answer : \ n^2 +4n -12 =(n+6)(n-2)`