How to divide a polynomial by a binomial

'Cuemath's Dividing Polynomials by Binomials Calculator' is an online tool that helps to divide polynomials by binomials.

What is the Dividing Polynomials by Binomials Calculator?

 Cuemath's online dividing polynomials by binomials calculator helps you to divide polynomials by binomials within a few seconds.

How to Use Dividing Polynomials by Binomials Calculator?

Please follow the below steps to divide polynomials by binomials:

• Step 1: Enter the polynomial and binomial in the given input box.
• Step 2: Click on the "Divide" button to find division for polynomial and a binomial
• Step 3: Click on the "Reset" button to find the division for different polynomials and binomials

How to Find Dividing Polynomials by Binomials?  

A polynomial is defined as an algebraic expression that shows the sum of monomials. For example, y2+5, A binomial is defined as an algebraic expression with two terms. In general terms, a binomial is defined as the sum of two monomials. A Binomial is represented as ax+b. For example, 3x + 5

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Solved Example: 

Divide the given polynomial by a binomial (x2 + 6x + 9) / x + 3

Solution:

= (x2 + 6x + 9) / x + 3

=  (x + 3)2 / (x + 3)

= x + 3

Similarly, you can try the calculator to divide a polynomial and binomial

1) 4x3 + 5x2 + 7 / 5x + 3         2) 7x + 5x3 / 3x + 2

Video transcript

Divide x squared minus 3x plus 2 divided by x minus 2. So we're going to divide this into that. And we can do this really the same way that you first learned long division. So we have x minus 2 being divided into x squared minus 3x plus 2. Another way we could have written the same exact expression is x squared minus 3x plus 2, all of that over x minus 2. That, that, and that are all equivalent expressions. Now, to do this type of long division-- we can call it algebraic long division-- you want to look at the highest degree term on the x minus 2 and the highest degree term on the x squared minus 3x plus 2. And here's the x, and here's the x squared. x goes into x squared how many times? Or x squared divided by x is what? Well, that's just equal to x. So x goes into x squared x times. And I'm going to write it in this column right here above all of the x terms. And then we want to multiply x times x minus 2. That gives us-- x times x is x squared. x times negative 2 is negative 2x. And just like you first learned in long division, you want to subtract this from that. But that's completely the same as adding the opposite, or multiplying each of these terms by negative 1 and then adding. So let's multiply that times negative 1. And negative 2x times negative 1 is positive 2x. And now let's add. x squared minus x squared-- those cancel out. Negative 3x plus 2x-- that is negative x. And then we can bring down this 2 over here. So it's negative x plus 2 left over, when we only go x times. So then we say, can x minus 2 go into negative x plus 2? Well, x goes into negative x negative one times. You can look at it right here. Negative x divided by x is negative 1. These guys cancel out. Those guys cancel out. So negative 1 times x minus 2-- you have negative 1 times x, which is negative x. Negative 1 times negative 2 is positive 2. And we want to subtract this from that, just like you do in long division. But that's the same thing as adding the opposite, or multiplying each of these terms by negative 1 and then adding. So negative x times negative 1 is positive x. Positive 2 times negative 1 is negative 2. These guys cancel out, add up to 0. These guys add up to 0. We have no remainder. So we got this as being equal to x minus 1. And we can verify it. If we multiply x minus 1 times x minus 2, we should get this. So let's actually do that. So let's multiply x minus 1 times x minus 2. So let's multiply negative 2 times negative 1. That gives us positive 2. Negative 2 times x-- that's negative 2x. Let's multiply x times negative 1. That is negative x. And then x times x is x squared. And then add all the like terms. x squared, negative 2x minus x-- that's negative 3x. And then 2 plus nothing is just 2. And so we got that polynomial again.

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