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3.7 Divide Polynomials
Example 1 Divide a polynomial by a monomialDivide a polynomial by a monomialDivide 10x3 25x2 + 15x by 5x.
Solution Method 1: Write the division as a fraction. Method 1: Write the division as a fraction.
= Write as a fraction. Write as a fraction. xxx 152510 23
x5
Divide each term by _____. Divide each term by _____. x5= 310xx5
225xx5
x15
x5
= _______________2 2x 5 x 3 Simplify. Simplify.
xxxx 5 152510 23
3.7 Divide Polynomials
Example 1 Divide a polynomial by a monomialDivide a polynomial by a monomialDivide 10x3 25x2 + 15x by 5x.
Solution Method 2: Use long division. Method 2: Use long division.
xxxx 1525105 23
Think:
xx 510 3Think:
xx 525 2
22x x5 3
Think:
xx 515
_____________ 5 152510 23 xxxx 352 2 xx
3.7 Divide PolynomialsCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Divide (12x3 9x2 3x by 3x.
= 312xx3
29xx3
x3
x3
4 2x 3 x 1
3.7 Divide Polynomials
Example 2 Divide a polynomial by a binomialDivide a polynomial by a binomialDivide 2x2 + 9x – 6 by 2x + 3.
Solution First divide the first term of First divide the first term of 2x2 + 9x – 6 by the first term of 2x + 3. .
69232 2 xxxx Multiply __ and _______. Multiply __ and _______. x 32 x
22x x3
Subtract _________. Subtract _________. xx 32 2 6Bring down ____.Bring down ____.
x6 6Divide the first term of Divide the first term of ______ by the first term of ______ by the first term of 22xx + 3. + 3.
66 x
3
Multiply __ and _______. Multiply __ and _______. 3 32 xx6 9
Subtract _________. Subtract _________. 96 x
15
_____________ 32 692 2 xxx 3x32
15
x
3.7 Divide PolynomialsCheckpoint. Divide. Checkpoint. Divide.
73 143 .2 2 xxx
14 373 2 xxxx
23x x7 x6 14
2
x6 14 0
2x
3.7 Divide PolynomialsCheckpoint. Divide. Checkpoint. Divide.
53 11136 .3 2 xxx
1113653 2 xxxx2
26x x10 x3 11
1
x3 5 6
12 x53
6
x
Multiply __ and _______. Multiply __ and _______.
3.7 Divide Polynomials
Example 3 Insert missing termsInsert missing termsDivide 4x2– 11 by – 3 + 2x.
110432 2 xxxx2 Rewrite polynomials. Rewrite polynomials.
Insert missing terms Insert missing terms
x2 32 x24x x6 Subtract _________. Subtract _________. xx 64 2 Bring down ____.Bring down ____.11
x6 11
3
Multiply __ and _______. Multiply __ and _______. 3 32 xx6 9
Subtract _________. Subtract _________. 96 x
2
_____________ 23 114 2 xx 32 x32
2
x
3.7 Divide PolynomialsCheckpoint. Divide. Checkpoint. Divide.
xxx 2 26 .4 2
6 2 2 xxx
2x x2 x4 6
4
x4 8 14
4x
2x
2
14
x
3.7 Divide PolynomialsCheckpoint. Divide. Checkpoint. Divide.
xx 3 311 .5 2
11 03 2 xxx3
23x x9 x9 11
9
x9 27 16
93 x
3x
3
16
x
3.7 Divide Polynomials
Pg. 173, 3.7 #1 – 16
