SOLUTION
Write out the expression
[tex]4x^2-27x+18[/tex]step1: Multiply the coefficient of the first and last term
[tex]4x^2\times18=72x^2[/tex]Step2: Obtain the factors of the term above that can conveniently replace the second term n the expression
[tex]\begin{gathered} 72x^2=-24x\times-3x \\ -27x=-24x-3x \end{gathered}[/tex]Step3: Replace the second term with the two terms obtained
[tex]\begin{gathered} 4x^2-27x+18\text{ becomes } \\ 4x^2-24x-3x+18 \end{gathered}[/tex]Step4: Group the term and obtain the common factors
[tex]\begin{gathered} (4x^2-24x)-(3x+18) \\ 4x(x-6)-3(x-6) \\ (x-6)(4x-3) \end{gathered}[/tex]Hence the factors of the expression are (4x-3)(x-6)
The X- intercept is the point where the expression to zero
[tex]\begin{gathered} (4x-3)(x-6)=0 \\ \text{equate each to zero} \\ 4x-3=0\text{ or x-6=0} \\ 4x=3\text{ or x=6} \\ \text{Then } \\ x=\frac{3}{4},6 \end{gathered}[/tex]Hence the X-intercept is (3/4,0) and (6,0)
