Question

which process do you preferred in identifying if the binomial is a factor of the polynomial?​

Answer 1

Answer:

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.

Answer 2

Answer:

To identify if the binomial is a factor of the polynomial we apply factor theorem.

Step-by-step explanation:

Given: Binomial is a factor of the polynomial.

To find: The process used in identifying if the binomial is a factor of the polynomial.

Solution:

Algebraic expression with two terms is binomial and with two or more terms is called polynomial.

Using long division or synthetic division, we divide the polynomial by a binomial and if the remainder becomes zero, then the binomial used as the divisor is the factor of the polynomial.

But sometimes the remainder may not be zero.Then we apply factor theorem to identify that the binomial is a factor of the polynomial.

Factor Theorem: If f(x) is a polynomial of degree n≥1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a) =0.

In other words , a polynomial f(x) has a factor (x-a) if and only if f(a)=0.

Factor theorem is used when factoring polynomials completely and finding the roots of the polynomial.

By factor theorem we know that for any binomial g(x), whose root is a, if p(a) = 0 for another polynomial p(x), then g(x) is a factor of p(x).

Therefore to identify if the binomial is a factor of the polynomial we prefer factor theorem.

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