Pre-Cal Math Project

1. Multiplying Polynomials
Jessica Ada
Lia De Guzman
Camille Tugade
Nikko Salazar

2. - Simple Multiplying
- Multiplying Binomials
- Multiplying Trinomials
- Substitution
- Applying Polynomials to Geometry

3. Simple Multiplying
The Basics:
(11x)(10x + 9)= 110x² + 99x
(11x)(10x + 9)= 110x² + 99x
The first thing that you would do is multiply 11x and 10x. The
answer is 110x² because 11 times 10 is 110 and the first
variable from the first set of brackets gets multiplied by the
other on the next set of brackets, therefore having to multiply
“x” by “x” getting an answer of x². Don’t forget, you must
multiply the 11x by the last term on the binomial which in this
case would be 9.

4. Multiplying Binomials
Binomials:
(2x + 3) (13x – 5)
When multiplying binomials, you use the F.O.I.L method..
F: first (2x + 3) (13x – 5)
O: outer (2x + 3) (13x – 5)
I: inner (2x + 3) (13x – 5)
L: last (2x + 3) (13x – 5)
Multiplying the first terms together, the outer, inner, and the last
terms. Here, we have 2x multiplied by 13x which is 26x². Now,
multiply the outer terms, 2x and -5 which would give you -10x. Next
is the inner terms, 3 and 13x giving a product of 39x. Now, the last
two terms, 3 and -5 giving -15. Now put all your answers together.
You should have 26x² - 10x + 39x -15. From here, you must collect
your like terms and here we only have the -10x and +39x, giving us
a sum of 29x. Your final answer would be 26x² +29x -15.

5. Multiplying Trinomials
Trinomials:
(x + 3)(x² + 2x + 4) Once you finish multiplying
Multiplying a trinomial is similar everything with the first term on
to multiplying binomial. You the binomial, you multiply with
must multiply every term from the second term from the
the binomial by every term from binomial. Now do the same
the trinomial. So first you would process to get your needed
multiply the first terms together. answers.
(x + 3)(x² + 2x + 4)= x³. (x + 3)(x² + 2x + 4)=3x²
Multiply the next term, which is x Multiply the next term 3 and 2x.
and 2x. (x + 3)(x² + 2x + 4)= 6x
(x + 3)(x² + 2x + 4)=2x². Now multiply the last term which 3
Multiply the x and the very last and 4.
term of the trinomial, which you (x + 3)(x² + 2x + 4)= 12
would call a constant. Your answer should be :
(x + 3)(x² + 2x + 4)=4x. x³ + 5x² + 10x + 12

6. Substitution
Substitution
..Is the replacement of one thing with another.
Let’s say we are given something like this: x² - 5x + 6
And now we need to find out what it equals to when
we put a number in for “x”… like let “x” equal to 2.
Everywhere you see an “x” stick in a 2.
x² - 5x + 6 -> (2)² - 5(2) + 6.
When it’s solve it should look like this:
4 - 10 + 6 = 0

7. Applying Polynomials in Geometry
Let’s say that the length is 5x + 2 and the width is 2x.
5x + 2
2x
The formula for the area of a rectangle is A = L(W). Now, substitute
the given information onto your formula. Substituted, you should
have 2x(5x + 2). Looks familiar? This is just the multiplying
binomials again. When simplified, you should get 10x² +4x.