This week we completed chapter one of polynomials and continued with factoring them in chapter 2.
To factor a polynomial, you first need to find common factors, and find patterns within them.
Some can be solved by finding their specific factors, within the coefficients. You can use their common factors to divide every term of the polynomial, but you need to show it being multiplied by the same number, otherwise it would not become the same answer if flipped around.
But even after that, the factorization has not been complete. To know that you have completed a question, the variables need to have no exponents.
You can find the complete answer by finding a pattern. In the trinomial , it can be simplified to . This is because there are two x’s, making , the middle term comes from adding the 2 constants in the simplified polynomial, and the last one comes from multiplying them.
You can find numbers that follow this pattern in a polynomial quite quickly.
ex. (continuing first example)
This week we began our unit on polynomials. I learned how to group like terms and find specific degrees, coefficients, and kinds of polynomials (monomial, binomial, etc.) One of the things I learned on top of this was how to multiply polynomials using various methods. I will be showing how to use area cubes/squares and FOIL/claw method.
To use the area square method, you can take the specific terms and lay them outside of a square. The square is divided into 4 smaller squares, and outside of the squares lie the polynomials terms. One on the left side of the square, and one on the top. You put one piece of the term over one smaller square, and another over the other.
The squares align so that you can do the multiplication step by step, the two in the corner, both corners, top and bottom corners, etc.
Once you have all of the terms from the multiplication, you will most likely have like terms. You would need to group these like terms together to find the final answer.
The FOIL method stands for the order in which you multiply the numbers. F – first, O – outside, I – inside, L – last.
Just like the area square method, you multiply them, step by step to get the answer. But once again, you may have like terms that need to be grouped to find the final answer.
The FOIL method can also be called the claw method because of the way the lines look. The lined are made to visualize which terms multiply with which.