Week 6 – Math 10

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.

ex:

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 $x^2 + 5x + 4$, it can be simplified to $(x + 4)(x + 1)$. This is because there are two x’s, making $x^2$,  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)