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

1 Answer
Mar 10, 2018

#(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#