Question

How do you factor this trinomial?

10n^2 + n – 3

Step by step please ^^

Answer 1

First way
n = -5n + 6n


`10n^2+n-3=10n^2-5n+6n-3=5n(2n-1)+3(2n-1)=(2n-1)(5n+3)`

Second way

`f(x)=a(x-x_1)(x-x_2)` the formula


`an^2+bn+c=0\\\\ 10n^2+n-3=0`

a=10 , b=1 , c=-3


`\Delta=b^2-4ac=1^2-4\cdot 10\cdot (-3)=121\\\\ \sqrt\Delta=11`


`n_1=(-b-\sqrt\Delta)/(2a)=(-1-11)/(2\cdot 10)=(-12)/(20)=-(3)/(5)\\\\ n_2=(-b+\sqrt\Delta)/(2a)=(-1+11)/(2\cdot 10)=(10)/(20)=(1)/(2)`


`f(n)=10[n-(-(3)/(5))]\cdot (n-(1)/(2))\\\\ f(n)=10(n+(3)/(5))(n-(1)/(2))`
the answer 1
or

a = 10 = 5*2


`f(n)=5(n+(3)/(5))\cdot 2(n-(1)/(2))\\\\f(n)=(5n+3)(2n-1)`
the answer 2