Answer:
Factors of given equation \(4x^2+25x+6\) is \((x+6)(4x+1)\)
Step-by-step explanation:
Given: equation \(4x^2+25x+6\)
We have to factorize the given quadratic equation \(4x^2+25x+6\)
We will factorize the quadratic equation using middle term splitting method,
Factorize the coefficient of x in such a way so that the sum or difference of the terms gives the poduct of coefficient of \(x^2\) and constant term.
For given equation,
25x can be split as 24x + x
Equation can be written as,
\(4x^2+24x+x+6\)
taking 4x common from first two terms and 1 common from last two term , we have,
\(\Rightarrow 4x(x+6)+1(x+6)\)
Taking (x+6) common , we have
\(\Rightarrow (x+6)(4x+1)\)
Thus, factors of given equation \(4x^2+25x+6\) is \((x+6)(4x+1)\)
