This document is an algebra worksheet reviewing factoring techniques. It contains questions about factoring trinomials and finding greatest common factors. The questions involve identifying key terms in trinomials, factoring using greatest common factor and difference of squares methods, and determining what type of factors are needed based on the signs of terms in a trinomial.

1. Name ____________________________________ Date _____________________
Algebra 1B Worksheet Review unit 13 Form B
1. What does the abbreviation GCF stand for? Greatest Common Factor
2. Use factor trees to find the GCF for each set of numbers. ( Show the work )
a. 42 30 b. 18 72
3∙2∙7 5 ∙ 3∙ 2 3∙3∙2 2∙2∙2∙3∙3
a. ____3∙2 = 6________ b. ___3∙3∙2=18__________
3. Find the GCF for each set of monomials
a. 30a2d4 24ad4 b. -24a3b5 -12ab3
5∙2∙3 2∙2∙2∙3 -1∙2∙2∙2∙3∙a∙a∙a∙b∙b∙b∙b∙b, -1∙2∙2∙3∙a∙b∙b∙b
a. ___2∙3=6______________ b. _____-2∙2∙3∙a∙b∙b∙b=-12ab3_______
4. Use common factoring to reverse the distributive property in each problem.
a. 4wx + 12wy ___4w(x+3y)_________________
b. 5b - 15b2 _____5b(1-3b)____________________
c. 18a2 + 12a3 _____6a2(3 + 2a)___________________
d. wx + xy ____x(w + y)_____________
e. 14ax + 6ay - 4az ______2a (7x + 3y -2z)_______________
f. 3ax - 9a2x -15ax3 ____3ax(1 – 3a – 5x2)________________
g. 5a - 11b ______none_______________

2. 5. Circle the term in the trinomial we can call the SUM term x2 - 12x + 36
6. Circle the term in the trinomial we can call the PRODUCT term x2 + 12x - 45
7. The SUM term can also be called the __linear_______ term.
8. The PRODUCT term can also be called the ___constant____________ term.
9. If we multiply two numbers together and the answer is negative then the
signs were ___________________ ( same/different)
10.Find the asked for pair of numbers
a. Find a pair of factors that multiply to 12 and add up to 7. ____4,3_____________
b. Find a pair of factors that multiply to 42 and add up to -13. __-7. -6___________
c. Find a pair of factors that multiply to 30 and add up to 31. _____30, 1____________
d. Find a pair of factors that multiply to -20 and add up to 1. ____5, -4_________
11. If a trinomial has a negative PRODUCT ( last ) term then we need to find a
_________________________ pair of factors .
( positive or negative or mixed)
12. List the kind of pair of factors that we should use to reverse the FOIL multiplication in each
trinomial. ( Answer mixed, positive, or negative )
a. a2 + 14a +40 ___positive_________________
b. x2 + 7x - 18 _____mixed_______________
c. y2 - 10y + 24 ____negative________________
d. a2 - 9a + 8 _____negative_______________
e. x2 + 3x - 28 ____mixed________________
f. a2 + 9ab + 14b2 ____positive_____________
g. a2 - a - 56 _____mixed_______________

3. 13. Factor the following
a. x2 + 16x + 60 _(x + 10) (x + 6) _ b. y2 + 8y - 9 (y + 1) (y – 9)
c. 16a2 - 9b2 ___(4a + 3b) (4a – 3b)_ d. w2 - 13w + 22 (w – 11) (w – 2)
e. x2 + 12x + 35 _(x + 7) (x + 5) _ f. y2 - 4y - 21 (y – 7) (y + 3)
g. a2 - 100 ___(a + 10) (a – 10) h. w2 - 14w + 45 _(w -9) (w -5)
i. a2 - 18y + 81 _(a – 9) (a + 9) j. w2 - w - 30 _(w – 6) (w + 5)
k. a2 + 5a + 4 _(a + 4) (a + 1) l. x2 + 14x + 49 _(x + 7) (x + 7)
Factor the following.
a. 3x2 + 10x + 7 _(3x + 7) (x + 1) b. 2x2 - 11x + 5 _(2x - 1) (x – 5)
c. 5a2 + 12a + 4 _(5a + 2) (a + 2) d. 4y2 - 17y + 15 _(4y – 5) (y – 3)
e. 3x2 + 10x - 8 _(3x –2) (x + 4) f. 7a2 - 18a - 9 _(7a + 3) (a – 3)