# Math

Part 1: Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

I do not get this at all and help would mean so much

1. 👍
2. 👎
3. 👁
1. the divisor is a factor if the remainder is zero

Just as you know that 5 is a factor of 35 because 35/5 has zero remainder.

For example,

(2x-1)(x+2)(3x+7) / (x+2)
= (6x^3+23x^2+15x-14)/(x+2)

we know that the remainder is zero, because we constructed it that way. To make that a fraction where the divisor is NOT a factor, just change any of the coefficients. Then the divisor will no longer go in evenly.

1. 👍
2. 👎

## Similar Questions

1. ### algebra

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 2 – 11x^2 – 8x + 6x^2 A. –5x^2 – 8x + 2; quadratic trinomial B. –5x^2 – 8x; quadratic binomial C. –6x^2 – 8x

2. ### Algebra 1

Just checking my answers. What is the sum or difference? 1. 2x^4 - 8x^4 A. -6x^8 B. -6x^4*** C. -16x^4 D. -16x^8 What is the sum or difference 2. 10y^10 - 14y^10 A. -4y^20 B. -140y^20 C. -140y^10 D. -4y^10*** 3. Write the

3. ### algebra

Please help!!! Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they

4. ### Math

How did the Hunter get hurt while benind over to study some tracks? Algebra with Pizzazz! pg 123 OBJECTIVE: to divide a polynomial by a binomial EX: (x^2+8x+150/(x+5)

1. ### calculus

Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=-3, f''(0)=1, and f'''(0)=4. Write the third-degree Taylor polynomial for h, where h(x) = integral of f(t)dt from 0 to x, about x=0

2. ### statistics

Answer the following: (A) Find the binomial probability P(x = 5), where n = 12 and p = 0.70. (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. (C) How would you find the normal

3. ### Algebra

Use synthetic division to divide the polynomial 2x^3 – 12x – 5 by x + 4, Write the quotient polynomial and the remainder. [Be careful – notice that there is no x2 term.]. Show work.

4. ### Math

Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots

1. ### algebra

Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1. 7a^2b + 3b^2 – a^2b 2. 6g^2h^3k

2. ### Algebra

Give the degree and classify the polynomial by the number of terms. A. degree: 2; trinomial B. degree: 3; binomial C. degree: 3; trinomial D. degree: 2; binomial Is B correct?

3. ### Math2

The product of a monomial and a binomial is a _____. Which words correctly fill in the blank? Select all correct answer choices. A)binomial B)monomial C)polynomial D)trinomial E)variable I'm pretty sure it's A) and B), but is C)

4. ### math

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a). Part 1. Show all work using long division to divide your polynomial by the binomial. Part 2. Show all work to evaluate f(a) using the