(x%2B3)(x-4)-in-standard-form.jpeg "(x+1)(x+3)(x-4) In Standard Form")
Expanding (x+1)(x+3)(x-4) into Standard Form
To express the polynomial (x+1)(x+3)(x-4) in standard form, we need to perform the necessary multiplications and combine like terms.
Step 1: Multiply the first two factors
Let's start by expanding the product of (x+1) and (x+3):
(x+1)(x+3) = x(x+3) + 1(x+3) = x² + 3x + x + 3 = x² + 4x + 3
Step 2: Multiply the result by the third factor
Now, we multiply the result from Step 1, (x² + 4x + 3), by (x-4):
(x² + 4x + 3)(x-4) = x²(x-4) + 4x(x-4) + 3(x-4) = x³ - 4x² + 4x² - 16x + 3x - 12 = x³ - 13x - 12
Conclusion
Therefore, the standard form of the polynomial (x+1)(x+3)(x-4) is x³ - 13x - 12.