Question

Please answer the following equation? 4x^2-27x+18Factor and solve for the x-intercept

Answer 1

Write out the expression

`4x^2-27x+18`

step1: Multiply the coefficient of the first and last term

`4x^2*18=72x^2`

Step2: Obtain the factors of the term above that can conveniently replace the second term n the expression

`\begin{gathered} 72x^2=-24x*-3x \\ -27x=-24x-3x \end{gathered}`

Step3: Replace the second term with the two terms obtained

`\begin{gathered} 4x^2-27x+18\text{ becomes } \\ 4x^2-24x-3x+18 \end{gathered}`

Step4: Group the term and obtain the common factors

`\begin{gathered} (4x^2-24x)-(3x+18) \\ 4x(x-6)-3(x-6) \\ (x-6)(4x-3) \end{gathered}`

Hence the factors of the expression are (4x-3)(x-6)

The X- intercept is the point where the expression to zero

`\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=(3)/(4),6 \end{gathered}`

Hence the X-intercept is (3/4,0) and (6,0)