dividing polynomials mr. richard must have your “un-divided” attention for this lesson!
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DIVIDING POLYNOMIALS
Mr. Richard must have your “Un-Divided” attention for this
lesson!
Algebraic long division
Divide 2x³ + 3x² - x + 1 by x + 2
3 22 2 3 1x x x x x + 2 is the divisor
The quotient will be here.
2x³ + 3x² - x + 1 is the dividend
Algebraic long division
First divide the first term of the dividend, 2x³, by x (the first term of the divisor).
3 22 2 3 1x x x x
22xThis gives 2x². This will be the first term of the quotient.
Algebraic long division
Now multiply 2x² by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2xand subtract
Algebraic long division
Bring down the next term, -x.
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
Algebraic long division
Now divide –x², the first term of –x² - x, by x, the first term of the divisor
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
which gives –x.
Algebraic long division
Multiply –x by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
xand subtract
Algebraic long division
Bring down the next term, 1 x
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
1
Algebraic long division
Divide x, the first term of x + 1, by x, the first term of the divisor
13 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x 1which gives 1
Algebraic long division
Multiply x + 2 by 1
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x
1
12x 1and subtract
Algebraic long division
The remainder is –1.
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x
1
12x 1
The quotient is 2x² - x + 1
Try This One Yourself!
Try This ONE! 2
822
x
xx
822 2 xxxx
xx 22 x4 8
4
84 x0
Check
)2)(4( xx
8422 xxx
822 xx
x
x2
)2(xx
x
x4 )2(4 x
Try This One!1
124
x
xx
1001 234 xxxxx
3x
34 xx 3x 2x
2x
23 xx 22x x0
x2 x2
xx 22 2 x2 1
2
22 x3
1
3
x
Time 4 U 2 Get 2 Work!
• Quiz: Page 324 # 2, 4, 6, 8, 10
• Homework # 1, 3, 5, 7, 11
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