Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial?
School Subject is not the name of your school!
first one
Create a sample problem that has a binomial which IS a factor of the polynomial being divided,
start with your polynomial in factored for, make up anything where one is a "binomial" say
(x2+2x+1)(x−4)
multiply out, and then you will be sure that x−4 is a factor of your result
just found this on another website. hope this helps!
you know it is a factor if the remainder is zero.
To determine if a binomial is a factor of a polynomial, you can use the division algorithm, commonly known as polynomial long division. Here's how you can approach this:
1. Identify the dividend, which is the polynomial you want to divide.
2. Identify the divisor, which is the binomial.
3. Set up the division problem by aligning the terms properly. Make sure the terms are arranged in descending order of their exponents.
4. Divide the first term of the dividend by the first term of the divisor. This will give you the first term of the quotient.
5. Multiply the entire divisor by the first term of the quotient and subtract it from the dividend.
6. Bring down the next term from the dividend and repeat steps 4 and 5 until you have exhausted all the terms in the dividend.
7. If the remainder is zero and there is no leftover term, then the binomial is a factor of the polynomial. In this case, the quotient will be the division result.
8. If there is a non-zero remainder or some leftover terms after division, the binomial is not a factor of the polynomial.
By performing polynomial long division, you can determine whether a binomial is a factor of a polynomial and obtain the quotient and remainder in the process.