(x%2B2)(x-3)-in-standard-form.jpeg "(3x+1)(x+2)(x-3) In Standard Form")
Expanding (3x+1)(x+2)(x-3) into Standard Form
This article will guide you through the process of expanding the expression (3x+1)(x+2)(x-3) into its standard form, which is a polynomial written in descending order of exponents.
Step 1: Multiply the first two factors
We begin by multiplying the first two factors, (3x+1) and (x+2), using the FOIL method (First, Outer, Inner, Last):
(3x+1)(x+2) = 3x² + 6x + x + 2 = 3x² + 7x + 2
Step 2: Multiply the result by the remaining factor
Now we multiply the result from step 1 (3x² + 7x + 2) by the remaining factor (x-3):
(3x² + 7x + 2)(x-3) = 3x³ - 9x² + 7x² - 21x + 2x - 6
Step 3: Combine like terms
Finally, we combine the like terms to get the expression in standard form:
3x³ - 9x² + 7x² - 21x + 2x - 6 = 3x³ - 2x² - 19x - 6
Therefore, the standard form of (3x+1)(x+2)(x-3) is 3x³ - 2x² - 19x - 6.