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ALGEBRA 1: CH.8
FACTORING BINOMIALS AND TRINOMIALS
Factor the binomial using greatest
common factor.
NAME:
Factor each binomial using a
diamond problem and either a
generic rectangle or factor by
grouping.
1. 9x2 + 12x =
Factor each trinomial using a
diamond problem and either a
generic rectangle or factor by
grouping. CAUTION: you may first
have to rewrite the expression so it is in
the correct order!!
11. 4x2 – 49 =
20. 2x – 3 + 8x2 =
Factor each binomial using the
GCF (Greatest Common Factor.)
Check your work by applying the
distributive property. You do not
21. 7 + x2 – 8x =
12. 25x2 – 1 =
have to use a generic rectangle and
diamond problem!
2. 15x2 + 10x = ___(
)
3. 12x2 + 6x + 3 = ___(
4. -4x – 12 = ___(
2
)
22. 6x2 + 10 + 19x =
)
5. 24x3+8x2 – 4x= __(
6. 4xy + 10x = ___(
7. 20x2 y+ 8xy = ___(
)
)
have to use a generic rectangle and
diamond problem!
13. 36x2 – 49 = (
)
2
9. 30x y+ 10xy = ___(
10. 20y – 40y = ___(
23. 12x2 – 17x – 5 =
)
8. -21xy – 6y + 15x = __(
2
Factor each binomial using the
pattern found above (called a
“difference of squares.”) You do not
)
)
14. 81x2 – 4 = (
)(
)
)(
)
15. x2 – 121 = (
)(
)
16. 25x2 – 49 = (
)(
)
17. 100x2 – 81 = (
)(
)
24. x + 10x2 – 21 =
CHECK ANSWERS #1-10:
-4
-3
3
2x
3x
4x
5x
4xy
10xy
20y
x2 + 3
4x2 + 2x + 1
3x + 4
3x + 2
2y + 5
7xy + 2y – 5x
3x + 1
6x2 + 2x – 1
y–2
5x + 2
18. x2 – 1 = (
)(
)
19. 4x2 – 9 = (
)(
)
CHECK ANSWERS #11-19:
2x + 3
10x + 9
9x + 2
x + 11
x+1
2x + 7
5x + 7
6x + 7
5x + 1
9x – 2
10x – 9
x – 11
x–1
2x – 7
2x – 3
6x – 7
5x – 1
5x – 7
25. –11x + x2 + 10 =
CHECK ANSWERS #20-25:
4x + 3
2x + 3
4x + 1
x – 7 3x + 2 3x – 5
2x – 1 x – 1 2x + 5
5x – 7 x – 1 x – 10