# Determine if a Polynomial q/(q^2+5q+6)*1/(q^2+3q+2)

qq2+5q+6⋅1q2+3q+2
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.
Factor q2+5q+6 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 6 and whose sum is 5.
2,3
Write the factored form using these integers.
q(q+2)(q+3)⋅1q2+3q+2
q(q+2)(q+3)⋅1q2+3q+2
Factor q2+3q+2 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 2 and whose sum is 3.
1,2
Write the factored form using these integers.
q(q+2)(q+3)⋅1(q+1)(q+2)
q(q+2)(q+3)⋅1(q+1)(q+2)
Multiply q(q+2)(q+3)⋅1(q+1)(q+2).
Multiply q(q+2)(q+3) and 1(q+1)(q+2).
q(q+2)(q+3)((q+1)(q+2))
Raise q+2 to the power of 1.
q(q+2)1(q+2)(q+3)(q+1)
Raise q+2 to the power of 1.
q(q+2)1(q+2)1(q+3)(q+1)
Use the power rule aman=am+n to combine exponents.
q(q+2)1+1(q+3)(q+1)
q(q+2)2(q+3)(q+1)
q(q+2)2(q+3)(q+1)
q(q+2)2(q+3)(q+1)
Determine if the expression breaks any of the rules.
Breaks rule 2
Determine if the expression is a polynomial.
Not a polynomial
Determine if a Polynomial q/(q^2+5q+6)*1/(q^2+3q+2)