(x%2B2)(x-3)-in-standard-form.jpeg "(x-1)(x+2)(x-3) In Standard Form")
Expanding (x-1)(x+2)(x-3) into Standard Form
In mathematics, a polynomial in standard form is written in descending order of exponents, with each term separated by a plus or minus sign. Let's expand the expression (x-1)(x+2)(x-3) and present it in standard form.
Step 1: Expand the first two factors
We can expand the first two factors using the distributive property (also known as FOIL):
(x-1)(x+2) = x(x+2) - 1(x+2) = x² + 2x - x - 2 = x² + x - 2
Step 2: Multiply the result by the third factor
Now we need to multiply the result from step 1 by the third factor (x-3):
(x² + x - 2)(x-3) = x²(x-3) + x(x-3) - 2(x-3) = x³ - 3x² + x² - 3x - 2x + 6 = x³ - 2x² - 5x + 6
The Final Result
Therefore, the expanded form of (x-1)(x+2)(x-3) in standard form is x³ - 2x² - 5x + 6.