We want to multiply the monomial 
by the monomial 
.
Remember that to multiply monomials we need to use the laws of exponents; in this case, the law for multiplying powers with the same base. The rule says that, when you multiply powers of the same base, you just need to add the exponents: 
, 
. Also, is worth pointing out that the exponent of a variable with no exponent is 1: 
.
Remember that we also need to multiply their coefficients , which are the numbers that multiply the variables; again, variables with no numbers have a coefficient of 1, so 
. Multiply coefficients is easy, you just need to multiply them as you usually do with everyday numbers.
Let's apply all of that to our multiplication:
We can conclude that 2x times x squared is 2x cubed.
Given:
The volume of the rectangular prism is
,
the height is h=(b+3)
1. The volume of a rectangular prism is (base area)*height
also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be
2
notice that
is the product of the largest 2 terms:
and b, so m must be 1
also, notice that 12 is the product of the constants, k and 3
so k*3=12, this means k=4
3
we write the above equality again:
=
4
now compare the coefficient with the left side:
8=n+3
n=5
substituting n=5:
the base area is
Answer:
