Question

which is the factorization of $8x^2 + 13x - 6$?
\bigcirc $(8x - 3)(x + 2)$
\bigcirc $(x - 6)(8x + 1)$
\bigcirc $(2x - 2)(4x + 3)$
\bigcirc $(4x - 1)(2x + 6)$

Explanation:

Step1: Expand each option

• For option \((8x - 3)(x + 2)\):

Using the distributive property \((a+b)(c+d)=ac+ad+bc+bd\), we have \(8x\times x+8x\times2-3\times x - 3\times2=8x^{2}+16x - 3x-6 = 8x^{2}+13x - 6\).

• For option \((x - 6)(8x + 1)\):

\(x\times8x+x\times1-6\times8x - 6\times1=8x^{2}+x-48x - 6=8x^{2}-47x - 6\).

• For option \((2x - 2)(4x + 3)\):

\(2x\times4x+2x\times3-2\times4x - 2\times3=8x^{2}+6x - 8x - 6=8x^{2}-2x - 6\).

• For option \((4x - 1)(2x + 6)\):

\(4x\times2x+4x\times6-1\times2x - 1\times6=8x^{2}+24x - 2x - 6=8x^{2}+22x - 6\).

Answer:

(8x - 3)(x + 2)