Question

How do you factor \[{x^2} - 36 = 0\] ?

Answer 1

Hint: In this question, we are given a polynomial equation, the highest exponent in the given equation is 2, so the degree of the equation is 2, hence the given equation is quadratic and has two solutions, by the solutions of the equation, we mean the values of the x for which the function given as $ f(x) = {x^2} - 36 $ has a value zero or when we plot this function on the graph, we see that the solutions of this function are the points on which the y-coordinate is zero, thus they are simply the x-intercepts.

Complete step-by-step answer:
We know that the standard form of a quadratic polynomial is $ a{x^2} + bx + c = 0 $ , factoring or completing the square method or the quadratic formula are the methods that are usually used to find the solutions/root/factors of a quadratic equation. But in this question, when we compare the given equation with the standard form, we see that the value of b is equal to zero that’s why we simply bring c to the other side of the equal to sign and divide both sides by a, then square rooting both the sides of the equation we get the roots
We are given –
 $
  {x^2} - 36 = 0 \\
   \Rightarrow {x^2} = 36 \\
   \Rightarrow x = \pm \sqrt {36} \\
   \Rightarrow x = \pm 6 \;
  $
Hence the factors of the equation $ {x^2} - 36 $ are $ x - 6 = 0 $ and $ x + 6 = 0 $ .
So, the correct answer is “ $ x - 6 = 0 $ and $ x + 6 = 0 $ ”.

Note: We can also solve the given equation by using an arithmetic identity, according to which the difference of the square of one number a and the square of another number b is equal to the product of the difference of a and b and the sum of a and b, that is, $ {a^2} - {b^2} = (a - b)(a + b) $ .