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Chapter 0: Problem 50

Factor each perfect square trinomial. $$x^{2}+4 x+4$$

Short Answer

Expert verified
The factor of the perfect square trinomial \(x^{2}+4x+4\) is \((x + 2)^{2}\).

Step by step solution

01

Identifying a and b

From the perfect square trinomial \(x^{2}+4x+4\), it can be seen that \(a^{2}=x^{2}\), which gives \(a=x\) and \(b^{2}=4\), which gives \(b=2\). Next, it has to be confirmed that 2ab equals the coefficient of x.
02

Confirming the Value of 2ab

The expression for 2ab is \(2*x*2 = 4x\). As it matches with the coefficient of x from the perfect square trinomial, we confirm that the trinomial is indeed a perfect square.
03

Factorizing the Perfect Square Trinomial

After confirming the values of a and b, the trinomial \(x^{2}+4x+4\) can be factorized to \((x + 2)^{2}\).

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Most popular questions from this chapter

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{4}}=-2$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$6+\frac{1}{x}=\frac{7}{x}$$

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x^{3}-64=(x+4)\left(x^{2}+4 x-16\right)$$

Describe ways in which solving a linear inequality is different than solving a linear equation.
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