Questions: Factor the following polynomial. 4 x^2-4 x+1 ([?] x-square)^2

Factor the following polynomial. 4 x^2-4 x+1 ([?] x-square)^2
Transcript text: Factor the following polynomial. \[ \begin{array}{l} 4 x^{2}-4 x+1 \\ ([?] x-\square)^{2} \end{array} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Polynomial

We start with the polynomial given by:

\[ 4x^2 - 4x + 1 \]

Step 2: Recognize the Perfect Square Trinomial

The polynomial can be recognized as a perfect square trinomial. A perfect square trinomial takes the form:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

In our case, we can identify:

  • \(a = 2x\) (since \((2x)^2 = 4x^2\))
  • \(b = 1\) (since \(1^2 = 1\))

The middle term \(-4x\) corresponds to \(-2ab\), where \(2ab = 4x\).

Step 3: Factor the Polynomial

Using the identified values of \(a\) and \(b\), we can factor the polynomial as follows:

\[ 4x^2 - 4x + 1 = (2x - 1)^2 \]

Final Answer

Thus, the factored form of the polynomial is:

\[ \boxed{(2x - 1)^2} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Use the graph of f to estimate the local extrema. The local extrema are □ (Use a comma to separate answers as needed. Round to the nearest integer.)
failedAnswered
Flint, chert, and jasper are microcrystalline forms of - hematite (Fe2O3) - quartz (SiO2) - calcite (CaCO3) - halite (NaCl)
failedAnswered
Side length: square m
failedAnswered
The heat of fusion ΔHf of acetone (OCC3(CH3)2) is 5.7 kJ / mol. Calculate the change in entropy ΔS when 20 g of acetone freezes at -94.7 C. Be sure your answer contains a unit symbol and the correct number of significant digits.
failedAnswered
Select all that apply What hormones are secreted by chromaffin cells of the adrenal medulla? Epinephrine Norepinephrine Aldosterone Thyroxine