What is the proof of factor theorem?

What is the proof of factor theorem?

The proof of The Factor Theorem is a consequence of what we already know. If (x−c) is a factor of p(x), this means p(x)=(x−c)q(x) for some polynomial q. Hence, p(c)=(c−c)q(c)=0, so c is a zero of p. Conversely, if c is a zero of p, then p(c)=0.

How do you prove a polynomial is a factor?

Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus “x minus the number” is a factor.

What is the concept of factoring polynomials?

Definitions: Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying.

Why is it important to understand the concept of factoring polynomials?

Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information.

Can you relate the concept of factoring polynomials in real life situations in what way?

Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time and making calculations during travel.

What is factor theorem in simple words?

From Wikipedia, the free encyclopedia. In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if (i.e. is a root).

What is factor theorem formula?

What is the Factor Theorem Formula? As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y).