Question

1.1
fill in the blank 2.5 points
factor to find the zeros of the function:
50x³ - 18x = 0
answers should be written as x=#,# with no spaces. write fractions as #/#.
for example, if your answer was x = 2 and x = -3/4, you would write your answer as x=2,3/4
type your answer...
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desk 1

Explanation:

Step1: Factor out common term

First, factor out the greatest common factor (GCF) from \(50x^3 - 18x\). The GCF of \(50x^3\) and \(18x\) is \(2x\). So we have:
\(2x(25x^2 - 9) = 0\)

Step2: Factor the difference of squares

Notice that \(25x^2 - 9\) is a difference of squares, which can be factored as \((a^2 - b^2)=(a - b)(a + b)\). Here, \(a = 5x\) and \(b = 3\), so:
\(2x(5x - 3)(5x + 3)=0\)

Step3: Solve for \(x\)

Set each factor equal to zero and solve for \(x\):

• For \(2x = 0\), we get \(x = 0\).
• For \(5x - 3 = 0\), add 3 to both sides: \(5x = 3\), then divide by 5: \(x=\frac{3}{5}\).
• For \(5x + 3 = 0\), subtract 3 from both sides: \(5x=-3\), then divide by 5: \(x = -\frac{3}{5}\).

Answer:

x=0,3/5,-3/5