(x+1)(x-5)

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, …).

Expand (x+1)(x-5) using the FOIL Method.

Apply the distributive property.

x(x-5)+1(x-5)

Apply the distributive property.

x⋅x+x⋅-5+1(x-5)

Apply the distributive property.

x⋅x+x⋅-5+1x+1⋅-5

x⋅x+x⋅-5+1x+1⋅-5

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅-5+1x+1⋅-5

Move -5 to the left of x.

x2-5⋅x+1x+1⋅-5

Multiply x by 1.

x2-5x+x+1⋅-5

Multiply -5 by 1.

x2-5x+x-5

x2-5x+x-5

Add -5x and x.

x2-4x-5

x2-4x-5

x2-4x-5

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+1)(x-5)