Question

If 4x² – 6x – m is divisible by x – 3, then m = ________.

Answer 1

Let f(x) = 4x² – 6x – m

It is given that f(x) is divisible by x – 3.

Therefore, $f\left(x\right)=0\mathrm{when}x=3$.

On putting x = 3 in f(x) = 0, we get

$$\begin{gathered} 4{\left(3\right)}^2-6\left(3\right)-m=0 \\ \Rightarrow 4\left(9\right)-6\left(3\right)-m=0 \\ \Rightarrow 36-18-m=0 \\ \Rightarrow 18-m=0 \\ \Rightarrow m=18 \end{gathered}$$

Hence, if 4x² – 6x – m is divisible by x – 3, then m = 18.