Question

check whether 4+3x is a factor of 3x3+7​

Answer 1

Step-by-step explanation:

Step 1 : If f(-c)=0, then (x+ c) is a factor of the polynomial f(x).

Step 2 : If p(d/c)= 0, then (cx-d) is a factor of the polynomial f(x).

Step 3 : If p(-d/c)= 0, then (cx+d) is a factor of the polynomial f(x).

Step 4 : If p(c)=0 and p(d) =0, then (x-c) and (x-d) are factors of the polynomial p(x).

Rather than finding the factors by using polynomial long division method, the best way to find the factors are factor theorem and synthetic division method. This theorem is used primarily to remove the known zeros from polynomials leaving all unknown zeros unimpaired, thus by finding the zeros easily to produce the lower degree polynomial.

There is another way to define the factor theorem. Usually, when a polynomial is divided by a binomial, we will get a reminder. The quotient obtained is called as depressed polynomial when the polynomial is divided by one of its binomial factors. If you get the remainder as zero, the factor theorem is illustrated as follows:

The polynomial, say f(x) has a factor (x-c) if f(c)= 0, where f(x) is a polynomial of degree n, where n is greater than or equal to 1 for any real number, c.