# Determine if a Polynomial (x-6)(3x-3)

(x-6)(3x-3)
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify the expression.
Expand (x-6)(3x-3) using the FOIL Method.
Apply the distributive property.
x(3x-3)-6(3x-3)
Apply the distributive property.
x(3x)+x⋅-3-6(3x-3)
Apply the distributive property.
x(3x)+x⋅-3-6(3x)-6⋅-3
x(3x)+x⋅-3-6(3x)-6⋅-3
Simplify and combine like terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
3x⋅x+x⋅-3-6(3x)-6⋅-3
Multiply x by x by adding the exponents.
Move x.
3(x⋅x)+x⋅-3-6(3x)-6⋅-3
Multiply x by x.
3×2+x⋅-3-6(3x)-6⋅-3
3×2+x⋅-3-6(3x)-6⋅-3
Move -3 to the left of x.
3×2-3⋅x-6(3x)-6⋅-3
Multiply 3 by -6.
3×2-3x-18x-6⋅-3
Multiply -6 by -3.
3×2-3x-18x+18
3×2-3x-18x+18
Subtract 18x from -3x.
3×2-21x+18
3×2-21x+18
3×2-21x+18
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Polynomial
Determine if a Polynomial (x-6)(3x-3)