diff --git a/homework5/Homework5_Q4.py b/homework5/Homework5_Q4.py
new file mode 100644
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+++ b/homework5/Homework5_Q4.py
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+import numpy as np
+import matplotlib.pyplot as plt
+
+def question_4():
+    # x = 1.920 -> 2.080 (included) step = 0.001
+    x = np.arange(1.920, 2.081, 0.001)
+    # p = [1, -18, 144, -672, 2016, -4032, 5376, -4608, 2304, -512]
+    # from x^9 to x^0
+    coeffs = [1, -18, 144, -672, 2016, -4032, 5376, -4608, 2304, -512]
+    p_coeff = np.polyval(coeffs, x)
+    # p(x) = (x-2)^9
+    p_fact = (x - 2.0) ** 9
+    plt.plot(x, p_coeff, label='Coefficient Form', lw=2)
+    plt.plot(x, p_fact, label='Factored Form', lw=2, ls='--')
+    plt.yscale('symlog', linthresh=1e-10)
+    plt.xlabel('x', fontsize=14)
+    plt.ylabel('p(x)', fontsize=14)
+    plt.title('Comparison of Polynomial Forms', fontsize=16)
+    # save the figure
+    plt.legend(fontsize=12)
+    plt.grid(True, which='both', ls='--', lw=0.5)
+    plt.savefig('question4.png')
+    plt.show()
+    abs_diff = np.abs(p_coeff - p_fact)
+    rel_diff = abs_diff / (np.abs(p_fact) + 1e-30)
+    print("Maximum Absolute Difference:", np.max(abs_diff))
+    print("Maximum Relative Difference:", (abs_diff[np.argmax(np.abs(p_fact))] /
+                               (np.abs(p_fact).max() + 1e-30)))
+
+if __name__ == "__main__":
+    question_4()
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diff --git a/homework5/question4.png b/homework5/question4.png
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diff --git a/homework5/question4.txt b/homework5/question4.txt
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+++ b/homework5/question4.txt
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+Maximum Absolute Difference: 1.1353085579642377e-11
+Maximum Relative Difference: 0.048289188322333074
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