Question

One of the factors of (36x² − 1) + (1 + 6x)² is

(a) (6x − 1)
(b) (6x + 1)
(c) 6x
(d) 6 − x

Answer 1

(b) (6x + 1)

$\left(36x^2-1\right)+{\left(1+6x\right)}^2=\left[{\left(6x\right)}^2-1^2\right]+{\left(1+6x\right)}^2$
$$\begin{gathered} =\left(6x+1\right)\left(6x-1\right)+{\left(6x+1\right)}^2 \\ =\left(6x+1\right)\left[\left(6x-1\right)+1\right] \\ =\left(6x+1\right)6x \end{gathered}$$

Hence, one of the factors of the given polynomial is (6x + 1).