Question

Factor the expression below.
4x^2-20x+25
0(4x+ 5)(x+5)
0(2x- 5)(2x-5)
0(4x-5)(x- 5)
0(2x+5)(2x+5)

Answer 1

To factor the expression \( 4x^2 - 20x + 25 \), we can start by recognizing that it is a quadratic in the form \( ax^2 + bx + c \).

1. **Identify coefficients**: Here, \( a = 4 \), \( b = -20 \), and \( c = 25 \).

2. **Calculate the discriminant**: The discriminant \( D \) can help determine if the quadratic factors neatly.
\[
D = b^2 - 4ac = (-20)^2 - 4(4)(25) = 400 - 400 = 0
\]
Since the discriminant is 0, the quadratic has a double root.

3. **Finding the root**: Use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{D}}{2a} = \frac{20 \pm 0}{2 \cdot 4} = \frac{20}{8} = 2.5
\]
The double root indicates that the quadratic can be expressed as:
\[
(x - 2.5)^2
\]

4. **Expressing in factored form**: Since \( 4x^2 - 20x + 25 \) can be viewed in terms of the double root:
\[
4(x - 2.5)^2
\]
To express this in a more standard factoring format, write \( 2.5 \) as \( \frac{5}{2} \):
\[
4 \left(x - \frac{5}{2}\right)^2 = (2x - 5)^2
\]

Thus, the factored form of \( 4x^2 - 20x + 25 \) is:
\[
(2x - 5)(2x - 5) \quad \text{or} \quad (2x - 5)^2
\]

From the provided options, the correct factorization is:
\[
0(2x - 5)(2x - 5)
\]
(Note: The presence of "0" in your options is confusing since the expression is not multiplied by 0; it should just be the factored form.)