Algebraic Manipulation Worksheets With Answers - Craven Community College Page 7
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29Dividing Polynomials
To divide a polynomial by a monomial, divide each term of the numerator by the denominator.
2
2
Example:
12X
Y – 6XY + 4X
2XY
2
2
12X
Y – 6XY + 4X
2XY
2XY 2XY
6X – 3 + 2X
Y
To divide one polynomial by another polynomial, use a method very similar to arithmetic long division.
2
X
Example:
Think X = X
2
Multiply (X – 3)(X) = X
– 3X
Subtract (X2 – 5X + 8) – (X2 – 3X) = -2X + 8
Repeat the three step process again
Remainder is written as a fraction
Exercises
Simplify each of the following
2
3
-3
4
4
2
1. (-2A
B)
2. (2X
Y
)(3X
Y
)
-1
2
2
-3
-2
3
5
2
6
3. (2X
Y
)(4X
Y
)
4. (10X
Y
)(21X
Y
)
-2
-2
-1
3
9
(12X
Y
)
(7XY
)(5X
Y)
3
2
2
2
2
2
5. (3X
– 2X
– 7) + (8X
– 8X + 7)
6. (-7X
+ 3X – 6) – (8X
– 4X + 7) + (3X
– 2X – 1)
3
2
7. (-2X
+ X
– 7)(2X – 3)
8. (2X – 7Y)(5X – 4Y)
2
3
2
9. (2X – 5)
10. (6X
+ 10X
– 32) ÷ (3X – 4)
2
2
11. A rectangle has a width of X
+ 7 and a length of X
+ 5X + 4. What is the perimeter of this
rectangle? What is the area?
12. Subtract the square of X – 6 from the square of X + 8.
2
13. What polynomial when divided by X – 7, yields a quotient of 2X
+ X – 6?
2
14. The area of a rectangle is 4X
+ 4X – 3. Find the width if the length is 2X + 3.
2
2
15. Two sides of a triangle are 3X
+ 2X + 1 and 4X
+ 7. Find the length of the third side if the
2
perimeter is 12X
+ 11X + 2.
7
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education