Question

How do you factor ${(3x - 5)^2}$ ?

Answer 1

In this question, we are given the square of the difference between two numbers and we have to find its factors. So we must know the type of this equation and the meaning of factors.
An algebraic expression is defined as an expression containing numerical values along with alphabets; when the alphabet representing an unknown variable quantity is raised to some non-negative integer as a power, a polynomial equation is obtained. Factors of a polynomial equation are defined as the values of the unknown variable for which the value of the function comes out to be zero.
They are also called the zeros/roots/solutions of the polynomial equation. The factors of an equation can be found out using the methods like factorization, completing the square, graphs and quadratic formula.

Complete step by step answer:
We have to find the factor of ${(3x - 5)^2}$
The given function is already simplified, so on putting it equal to zero, we get –
${(3x - 5)^2} = 0 \\\ \Rightarrow (3x - 5)(3x - 5) = 0 \\\ \Rightarrow 3x - 5 = 0,\,3x - 5 = 0 \\\ \Rightarrow x = \dfrac{5}{3},\,x = \dfrac{5}{3} \\\$
Hence the factors of the given equation are equal, that is, they both are equal to $x - \dfrac{5}{3} = 0$.

Note: We are given the square of $3x - 5$ , that is, $3x - 5$ multiplied with itself. The equation can be simplified by using the formula of finding the square of the difference of two numbers. But in this question, we don’t have to simplify the equation as we have to find its factors. So, it is solved by simply putting the equation equal to zero. On finding the square of $3x - 5$ , we will see that the equation is a quadratic equation, as it has a degree equal to 2, so the equation has 2 factors.