Question

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

${\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{12}\mathit{x}\mathbf{+}\mathbf{36}$is an example of a perfect square trinomial.

Short answer

The statement is true.

Step-by-step solution

Step 1. State the concept for factorization of algebraic expressions.

1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
2. If x is a variable and m, n are positive integers, then$x^{m+n}=(x^m\times x^n)$

Step 2. State the methods to factorize.

Factoring an algebraic expression means writing the expression as a product of factors.

To verify whether the factors are correct or not, multiply them and check if the result is the original algebraic expression.

Algebraic expressions can be factorized using the common factor method, regrouping like terms together, and also by using algebraic identities.

Step 3. Factorize the expression.

Factorizing the given trinomial:

$\begin{array}{c}{x}^2-12x+36=x^2-2.x.6+6^2\\ ={(x-6)}^2\\ =(x-6)(x-6)\end{array}$

Therefore, the given statement is true.