y = x⁴- 5x² + 4 represents the first graph.
y = x(x + 3)(x - 2) represents the second graph.
1) The first polynomial is;
y = x⁴- 5x² + 4
Simplifying this gives us;
y = x⁴- 4x² - x² + 4
y = x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Thus, the zeros of this polynomial are; x = -2, -1, 1, 2
From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So graph (1) represents the polynomial y = x⁴- 5x² + 4
2). The second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
Read more about Polynomial Graph at; https://brainly.com/question/14625910
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