Chapter 8: Q7. (page 513)

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$x^{2} - 12 x + 36$ is an example of a perfect square trinomial.

Short Answer

Expert verified

The statement is true.

Step by step solution

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

The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
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:

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

Therefore, the given statement is true.

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State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$x^{2} - 12 x + 36$ is an example of a perfect square trinomial.

Short Answer

Step by step solution

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

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

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State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.x2−12x+36is an example of a perfect square trinomial.

Short Answer

Step by step solution

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

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$x^{2} - 12 x + 36$ is an example of a perfect square trinomial.