(x-4)-polynomial-in-standard-form.jpeg "(x-3)(x-4) Polynomial In Standard Form")
Expanding the Polynomial (x - 3)(x - 4) to Standard Form
The given expression (x - 3)(x - 4) is a polynomial in factored form. To express it in standard form, we need to expand the product and combine like terms.
Expanding the Product
We can use the FOIL method (First, Outer, Inner, Last) to multiply the binomials:
- First: x * x = x²
- Outer: x * -4 = -4x
- Inner: -3 * x = -3x
- Last: -3 * -4 = 12
Combining the terms, we get:
x² - 4x - 3x + 12
Combining Like Terms
The terms -4x and -3x are like terms because they both have the variable 'x' raised to the power of 1. Combining these terms:
x² - 7x + 12
Standard Form
The polynomial (x - 3)(x - 4) in standard form is x² - 7x + 12.
The standard form of a polynomial arranges the terms in descending order of their exponents. In this case, the highest exponent is 2, followed by 1, and then 0 for the constant term.