SOLUTION
The given expression is
[tex]4x^2+8x-5[/tex]
The general trinomial expression is,
[tex]ax^2+bx+c[/tex]
Therefore,
[tex]\begin{gathered} a\times c=4\times-5=-20 \\ b=8 \end{gathered}[/tex]
Let us look for the factors of -20 and also confirm if the factors will give 8 as the sum.
[tex]\begin{gathered} -2\times10=-20 \\ -2+10=8 \end{gathered}[/tex]
Therefore, the two factors are -2 and 10.
Let us now replace 8x with -2x and 10x in the expression given
[tex]4x^2-2x+10x-5[/tex]
Break the expression into two groups
[tex]\mleft(4x^2-2x\mright)+\mleft(10x-5\mright)[/tex]
Factor out the common terms
[tex]2x(2x-1)+5(2x-1)[/tex]
Factor out the common term 2x - 1
[tex]\mleft(2x-1\mright)\mleft(2x+5\mright)[/tex]
Hence, the answer is
[tex]\mleft(2x-1\mright)\mleft(2x+5\mright)[/tex]
