Module 2
Adding and subtracting polynomials with algebra tiles
2 polynomials will be modeled through 2 separate algebra tile sets. When they are modeled out it is easier to add and subtract. For subtraction, subtract like algebra tiles from one another and the answer will be what is left. For addition, add the algebra tiles from both sides together. You basically ignore the addition sign and combine like terms. PAY ATTENTION TO THE SIGNS!
Multiplying 2 binomials
Apply the FOIL method to the two binomials the find the answer. Multiply the outside monomials together, along with the first, inside, and last monomials. Then add all of these together and simplify. When the expression can't be simplified anymore, the result will be the answer.
Adding and subtraction polynomials
In the polynomials given, find the like monomials and either add or subtract. What's left will be the answer
Finding the zeros of a function on a graph
The zeros of the function will be all the coordinates directly on the x-axis.
Multiplying polynomials using algebra tiles
This can usually be done without algebra tiles. Just apply the FOIL method to the 2 polynomials in separate parenthesis. When using algebra tiles you combine like terms to find the answer. You can tell the 2 polynomials represented in the algebra tiles by looking at the height and the base. The last row of tiles on the bottom will show the first polynomial in parenthesis. When like terms are combined at the bottom, it will equal the polynomial. The same for the height. The height will be the row furthest to the right. When like terms are combined, the answer will equal the second polynomial.
Adding polynomials to find the perimeter
To find the perimeter, you combine like monomials. You'll either add or subtract them depending on the signs. Ex: 1 side is 6b + 5 and another side is 10b + 5 those 2 sides together would be 16b + 10
Polynomials modeled through algebra tiles
To write out a polynomial using algebra tiles, all you have to do is combine like terms. If there are four x tiles then that means there will be a monomial of 4x
Finding the square of a binomial
When finding the square of a binomial you use the formula (a + b)^2 = a^2 + 2ab + b^2 All you have to do is plug a and b into the formula and simplify to get the answer Note: When you plug a into a^2, the entire thing is squared not just the variable. The whole number and the variable are multiplied by themselves.
Zero product property
When you have 2 binomials in separate parenthesis that are equal to 0 (aka a quadratic equation) you can solve it with the zero product property. The 2 binomials will be separated and will be equal to zero. Then you pretend that its a normal equation and solve for the variable. Ex: (3r + 2)(r + 3) = 0 3r + 2 = 0 and r + 3 = 0 r = -2/3 and r = -3
Multiplying polynomials by monomials
You will be given a monomial outside parenthesis and a polynomial inside parenthesis. Apply distributive property to get the answer. Whenever there is exponents you add them together. Ex: 3r^2(2r^2) = 6r^4