Final answer:
The polynomial y=(5x+7)(2x-1)(x-4) has a degree of 3, making it a cubic polynomial. This can be visualized with an equation grapher as part of learning about graphing polynomials.
Step-by-step explanation:
The degree of the polynomial y=(5x+7)(2x-1)(x-4) is determined by multiplying the degree of each individual term. When we multiply these terms, the degree of the polynomial is the sum of the degrees of the individual terms. Since the polynomial is a product of three terms, each with x to the power of 1 (which is the degree of a linear term), the degree of the polynomial is 1 + 1 + 1 = 3.
Hence, the polynomial y=(5x+7)(2x-1)(x-4) is a cubic polynomial with a degree of 3. When we use an equation grapher, we can visualize how the factors of the polynomial affect the shape of the curve on a graph. This is an example of graphing polynomials. Seeing the curves for individual terms like y = bx helps in understanding how these terms combine to form the overall shape of the polynomial curve.