Question

How do I factor 6x^2 + 13x +5

Answer 1

make the expression equal to 0
6x² + 13x + 5 = 0

since its in the for ax² + bx + c multiply 'c' by 'a' = 30
now you must find factors of 30 that multiply to give 5 but add to give 13 but since such an equation does't exist as whole numbers then you have to resort to using the formula which states that x =
`\frac{-b + or - \sqrt{b^(2) - 4ac } }{2a}`

so now you just plug in your values a = 6; b= 13 and c= 5

x =
`\frac{-13 + or - \sqrt{13^(2) - 4(6)(5) } }{2(6)}`

=
`(-13 + or - √(169 - 120 ) )/(12)`

∴ either x =
`(-13 + √(49 ) )/(12)` OR x =
`((-13) - √(49 ) )/(12)`

⇒ x = -
`(1)/(2)` OR x =
`- (5)/(3)`

∴ 6x² + 13x + 5 = (x +
`(1)/(2)`) (x +
`(5)/(3)`)