Download Wksh 7.5 - Mrs. Perior

Algebra IB
7.5 Worksheet
Name _________________________________
Date ___________________
Hour ______
FACTORING SPECIAL PRODUCTS
 I can factor perfect square trinomials. 
Determine whether each trinomial is a perfect square. If so, factor. If not, explain.
1. x2 – 4x + 4
2. x2 – 3x + 4
3. x2 – 14x + 49
4. 25x2 + 10x + 4
Factor each polynomial.
5. x2 + 10x + 25
6. x2 – 12x + 36
7. m2 + 16m + 64
8.
9. 4x2 – 4x + 1
10. 9x2 + 12x + 4
11. 25x2 + 20x + 4
12. 36x2 – 12x + 1
x2 – 24x + 144
13. A city purchases a square plot of land with an area of (x2 + 24x + 144) yd2 for a park. The dimensions of the
plot are of the form ax + b, where a and b are whole numbers.
a. Factor the trinomial to find an
expression for the side lengths of
the park.
b. Find an expression for the
perimeter of the park.
c. Find the perimeter when
x = 10 yd.
 I can factor the difference of two squares. 
Determine whether the binomial is a difference of perfect squares. If so, factor. If not, explain.
14. x2 – 4
15. x2 – 20
16. x2 – 81
17. x2 – 144
Factor each polynomial.
18. y2 – 64
19. x2 – 49
20. n2 – 81
21. x2 – 1
22. 36y2 – 25
23. 4x2 – 81
24. 25 – x2
25. 49x2 – 16
26. Fred designed a vegetable garden in the shape of a square and purchased fencing for that design. Then he
decided to change the design to a rectangle.
a. The square garden had an area of
x2 square feet. The area of the
rectangular garden is (x2 – 25)
square feet. Factor this expression.
b. The rectangular garden must
have the same perimeter as the
square garden, so Fred added a
number of feet to the length and
subtracted the same number of feet
from the width. Use your factors
from part (a) to determine how
many feet were added to the length
and subtracted from the width.
c. If the original length of the
square garden was 8 feet, what are
the length and width of the new
garden?
27. The area of a square is represented by 25x2 – 40x + 16.
a. What expression represents the
length of a side of the square?
b. What expression represents the
perimeter of the square?
c. What are the length of a side, the
perimeter, and the area of the square
when x = 3?