Question

Could you please help me with this problem? It’s about factoring?

Answer 1

The given expression is

`4x^2+8x-5`

The general trinomial expression is,

`ax^2+bx+c`

Therefore,

`\begin{gathered} a* c=4*-5=-20 \\ b=8 \end{gathered}`

Let us look for the factors of -20 and also confirm if the factors will give 8 as the sum.

`\begin{gathered} -2*10=-20 \\ -2+10=8 \end{gathered}`

Therefore, the two factors are -2 and 10.

Let us now replace 8x with -2x and 10x in the expression given

`4x^2-2x+10x-5`

Break the expression into two groups

`\mleft(4x^2-2x\mright)+\mleft(10x-5\mright)`

Factor out the common terms

`2x(2x-1)+5(2x-1)`

Factor out the common term 2x - 1

`\mleft(2x-1\mright)\mleft(2x+5\mright)`

Hence, the answer is

`\mleft(2x-1\mright)\mleft(2x+5\mright)`