Ryuk1990 said:Homework Statement
7X2(X - 2) - (X - 2)
2. The attempt at a solution
Ok, this is really simple but for some reason I can't figure out why the answer has to be (7X2 - 1)(X - 2)
The process is that I have to divide both parts by (X - 2). However, if I do that, I only get 7X2 - 1. Where does that (X - 2) come from for the final answer?
Factoring a polynomial is the process of breaking down a polynomial into smaller polynomials that can be multiplied together to obtain the original polynomial. It is essentially finding the factors or roots of the polynomial.
Factoring a polynomial is important because it allows us to simplify complex expressions and solve equations involving polynomials. It also helps us identify patterns and relationships between different polynomials.
The process of factoring a polynomial involves finding the greatest common factor (GCF) and then using various methods such as grouping, difference of squares, or trial and error to break down the polynomial into smaller factors.
Expanding a polynomial involves multiplying out all the terms in a polynomial, while factoring involves breaking down a polynomial into smaller factors. In other words, expanding goes from a simpler form to a more complex form, while factoring goes from a more complex form to a simpler form.
No, not all polynomials can be factored. Some polynomials, such as prime polynomials, have no factors other than 1 and itself. However, all polynomials with integer coefficients can be factored using methods such as the rational root theorem or the quadratic formula.