(x-2)(x-7)-in-standard-form.jpeg "(x+1)(x-2)(x-7) In Standard Form")
Expanding (x+1)(x-2)(x-7) into Standard Form
This article will guide you through the process of expanding the expression (x+1)(x-2)(x-7) into its standard form, which is a polynomial in descending order of exponents.
Step 1: Multiply the first two factors
Begin by multiplying the first two factors, (x+1) and (x-2), using the FOIL method (First, Outer, Inner, Last):
(x+1)(x-2) = x² - 2x + x - 2 = x² - x - 2
Step 2: Multiply the result by the remaining factor
Now, multiply the result from step 1 (x² - x - 2) by the remaining factor (x-7):
(x² - x - 2)(x - 7) = x²(x - 7) - x(x - 7) - 2(x - 7)
Step 3: Distribute and simplify
Distribute each term and combine like terms:
x²(x - 7) - x(x - 7) - 2(x - 7) = x³ - 7x² - x² + 7x - 2x + 14 = x³ - 8x² + 5x + 14
Conclusion
Therefore, the standard form of the expression (x+1)(x-2)(x-7) is x³ - 8x² + 5x + 14.