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POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Set both problems up using the long division format…numerator goes inside, denominator goes outside.
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Starting with the problem on the right, how many 24’s will dill divide 31 without going over ?
?
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Starting with the problem on the right, how many 24’s will dill divide 31 without going over ?
1…
1
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
You then multiply 1 x 24 and place it under the 31, and subtract.
1
- 24
7
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
For our algebra problem, we will always divide the first term of the numerator ( inside ) by the first term of the denominator ( outside).
1
- 24
7
xx
x2
2 2
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
That answer will fill in the first part of our answer.
1
- 24
7
xx
x2
2 2
x2
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Then you multiply that result by the outside...
1
- 24
7
x2
xxxx 6232 2
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
That result is subtracted just like the long division with numbers problem…...
1
- 24
7
x2
xxxx 6232 2
xx 62 2
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Here is where we must be careful !!!
1
- 24
7
x2
xx 62 2
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Here is where we must be careful !!!
The first terms will always subtract to be zero.
1
- 24
7
x2
xx 62 2
022 22 xx
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 31224
Here is where we must be careful !!!
The first terms will always subtract to be zero.
Then, you have a double negative sign when subtracting the next two terms…
1
- 24
7
x2
xx 62 2
022 22 xx
xxxxx 766
x7
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 312241
- 24
72
x2
xx 62 2
217 x
Bring down the next term in both…
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 312241
- 24
72
x2
xx 62 2
217 x
How many 24’s divide 72 ?
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
x2
xx 62 2
217 x
How many 24’s divide 72 ?
3…
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
x2
xx 62 2
217 x
Multiply and subtract…
- 72
0
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
x2
xx 62 2
217 x
Divide the first term of the new expression, by the first term of the outside…
- 72
0
77
x
x
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
72 x
xx 62 2
217 x
That result is the next part of the answer…
- 72
0
77
x
x
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
72 x
xx 62 2
217 x
Multiply that result by the outside…
- 72
0
21737 xx
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
72 x
xx 62 2
217 x
And place the result under the last expression and subtract…
- 72
0
21737 xx
217 x
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 :
3
212 2
x
xx
24
312
2123 2 xxx 3122413
- 24
72
72 x
xx 62 2
217 x
You should get the same expression. A double line shows no remainder
- 72
0217 x
POLYNOMIALS – Dividing By a Binomial
Dividing a polynomial by a binomial is similar to long division with numbers. In the first example, we’ll look at how they compare to each other.
EXAMPLE # 1 : 723
212 2
x
x
xx
2123 2 xxx
72 x
xx 62 2
217 x
You should get the same expression. A double line shows no remainder
217 x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
All expressions should be written in descending order. The expression in our numerator is missing the x1 term. Since it holds place value like a zero in the number 105, we need to show it as “0x” when doing our division
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Again we will begin by dividing the first term inside by the first term outside…
xx
x2
2
4 2
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
This result is the first part of our answer… x
x
x2
2
4 2
x2
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Multiply that result by the outside…
xxxx 104522 2
x2
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Multiply that result by the outside…and subtract
xxxx 104522 2
x2
xx 104 2
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Again, it is
x2
xx 104 2
xxx 10100
x10
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Bring down the next term…
x2
xx 104 2
2510 x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Divide the new first term by the outside first term…
x2
xx 104 2
2510 x
52
10
x
x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Divide the new first term by the outside first term…and place it in the answer
52 x
xx 104 2
2510 x
52
10
x
x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Multiply…
52 x
xx 104 2
2510 x
2510525 xx
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 :
52
254 2
x
x
250452 2 xxx
Multiply…and subtract
52 x
xx 104 2
2510 x
2510525 xx
2510 x
POLYNOMIALS – Dividing By a Binomial
Let’s try another…
EXAMPLE # 2 : 5252
254 2
xx
x
250452 2 xxx52 x
xx 104 2
2510 x2510 x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx2
3
33
xx
x
23x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
23x
232 3313 xxxx 23 33 xx
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
23x
22222 23535 xxxxx
23 33 xx 22x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
23x
23 33 xx
xx 62 2
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
xx 23 2
23 33 xx
xx 62 2 xx
x2
2 2
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
xx 23 2
23 33 xx
xx 62 2 xxxx 2212 2 xx 22 2
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
xx 23 2
23 33 xx
xx 62 2
xxx 426
xx 22 2
x4
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
xx 23 2
23 33 xx
xx 62 2 xx 22 2
44 x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
423 2 xx
23 33 xx
xx 62 2 xx 22 2
44 x 44
x
x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 :
1
4653 23
x
xxx
46531 23 xxxx
423 2 xx
23 33 xx
xx 62 2 xx 22 2
44 x44 x
POLYNOMIALS – Dividing By a Binomial
Sometimes there are more than three terms in our numerator. Just keep dividing any remainder’s first term by the outside’s first term
EXAMPLE # 1 : 4231
4653 223
xx
x
xxx
46531 23 xxxx
423 2 xx
23 33 xx
xx 62 2 xx 22 2
44 x44 x
