Question

How do you factor$16{x^2} - 1$?

Answer 1

Hint:To find the value of $x$, we need to move the $ - 1$ to the right-hand side and by taking square root on both sides, we can get the answer for this solution. Either we can solve by squaring on both sides or by moving the square to the right-hand side.

Complete step by step solution:
Let us consider the given equation,
$16{x^2} - 1$

Spend ten seconds and analyse the method by which it can be solved and then proceed.

Let us equate this to zero to find the factor for this problem,
$16{x^2} - 1 = 0$

Now we move the $ - 1$ to the right-hand side the equation becomes,
$16{x^2} = 1$

Bringing the $16$ to the right-hand side, it will become,
${x^2} = \dfrac{1}{{16}}$

Bringing square root to the right-hand side we get,

$
x = \dfrac{1}{{\sqrt {16} }} \\
x = \pm \dfrac{1}{4} \\
$
Here we got two values for $x$ which is equal to \[ - \dfrac{1}{4},\dfrac{1}{4}\]

Additional information: We solved this problem with no trouble because we only had two terms $16{x^2}$ and $1$. If we had three terms i.e.., ${x^2},x$ and constant term, then we have to use factorization methods to solve this problem. If we had three terms, then we have to use two steps to solve the problem. First step is to use synthetic division methods and then we have to use factorization methods to solve the problem.

Note: Whenever we bring the square to the right-hand side it will become square root and we get the two values for $x$ If you want to check whether the answer is correct or not, then substitute the value of $x$ in the question we will get zero.