Question

Which of the binomials below is a factor of this trinomial? 4x2 + 12x + 9A. 2x-3B. 2x-1C. 2x+1D. 2x+3

Answer 1

In order to factorate the trinomial, let's first find its roots using the quadratic formula:

`\begin{gathered} b^2-4ac=12^2-4\cdot4\cdot9=144-144=0 \\ x_1=x_2=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=(-12+0)/(2\cdot4)=-(12)/(8)=-(3)/(2) \end{gathered}`

Now we can write the trinomial in the form:

`a(x-x_1)(x-x_2)`

So we have that:

`4x2+12x+9=4(x+(3)/(2))(x+(3)/(2))=(2x+3)(2x+3)`

So 2x + 3 is a factor of the trinomial, therefore the answer is D.