Jun 23, 2025 · Multiply the factors: f (x) = (x2 + 1)(x2 − 4) = x4 − 3x2 − 4. The polynomial is x4 − 3x2 − 4 . Explanation Identify all roots We are given the roots i,−2, and 2 of a polynomial …

Nov 1, 2016 · For instance, the equation y = 3x2 − 6x + 3 has a discriminant of zero, indicating it touches the x-axis once, while y = 3x2 − 7x + 1 and y = 3x2 − 4x − 2 have positive …

Oct 28, 2024 · The cost is modeled by the polynomial 3x2 −160x + 300. Substitute x = 150 into the polynomial: Cost = 3(150)2 −160 × 150+ 300 Profit Calculation: Profit is the difference …

Mar 13, 2018 · The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and …

Nov 1, 2022 · The expression −3x2 + 12x can be factored as −3x(x − 4). This is done by finding the greatest common factor, which is −3x, and factoring it out. The result can be verified by …

Jul 14, 2016 · The solutions to the equation 3x2 − 12x + 24 = 0 are 2 + 2i and 2− 2i. This shows that the roots are complex numbers due to a negative discriminant. Therefore, the answer can …

May 4, 2022 · The expression 3x2 − 10x + 8 can be factored as (x − 2)(3x − 4). This involves finding two numbers that multiply to the product of the leading coefficient and the constant …

Mar 3, 2021 · The simplified form of the expression 2x − 3x2 + 8x + 7 is −3x2 + 10x +7. The coefficients that fill in the missing values are −3, 10, and 7.

Dec 7, 2016 · This means that in the polynomial equation 0 = 2+ 3x2 − 5x, the values for the coefficients and constant term are determined appropriately in the standard quadratic form.

Dec 14, 2016 · To solve the equation = x, we first rearrange it into standard form. Start by moving all terms to one side: 3x2 − 7x +3 = 0 Next, we can use the quadratic formula to find the …