Question

How do you factor the trinomial `4x^2 - 21x + 5 = 0`?

Answer 1

`(x-5)(4x-1)`

Explanation:

`"using the a-c method of factorising a quadratic"`

`"consider the factors of "(4xx5)" which sum to - 21"`

`"the factors of + 20 which sum to - 21 are - 20 and - 1"`

`"splitting the middle term gives"`

`4x^2-20x-x+5larrcolor(blue)"factor by grouping"`

`=color(red)(4x)(x-5)color(red)(-1)(x-5)`

`"take out common factor "(x-5)`

`(x-5)(color(red)(4x-1))`

`rArr4x^2-21x+5=(x-5)(4x-1)`

`"to solve the equation"`

`(x-5)(4x-1)=0`

`"equate each of the factors to zero and solve for x"`

`x-5=0rArrx=5`

`4x-1=0rArrx=1/4`