Review of Algebra 2: Factoring

Name ______Date ______Period ______

Factoring

*If you are absent the day we complete this handout together in class it is your responsibility to fill it in; please borrow from a friend to get the notes you missed!

Factoring Tips & Advice:

  • If there is an equal sign in the problem, be sure 0 is on a side by itself. If it’s not already there you must move around the terms until 0 is on a side by itself.
  • Begin ALL problems by pulling out the GCF if there is one.
  • If your highest powered term (ex. x2) is negative, factor out a “-1”
  • Factor:
  • If you have four terms, factor by grouping
  • If you have three terms (trinomial) factor accordingly:
  • 1x2 + bx + c  Think: What two numbers multiply to give “c” but add to give “b”.
  • ax2 + bx + c  First multiply “a” and “c” to give “d.” Think what two numbers when multiplied together give “d” but when added give “b.” These are NOT your answers! You use these numbers to rewrite the problem with two middle terms instead of one. Now you have four terms and can factor by grouping.
  • Special Cases: If your first term and last term are perfect squares you can use the formulas:
  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • Binomial Special Case: When there are only two terms and each term is a perfect squares and they are being subtracted (Does NOT work if adding), use the following formula:
  • a2 – b2 = (a – b)(a + b)
  • Perfect Cubes Special Case: Where you have a binomial and the first term AND the last term are perfect cubes you can use the following formulas to factor:
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • Lastly, if there was an equal sign in the problem you set factor equal to 0 separately and solve for the variable. These answers represent the

x-intercepts if the equation was graphed.

Completely factor and solve if necessary. SHOW ALL WORK ON COMPOSITION PAPER and keep in the notes section of your binder!

1.7x2 + 42x

2.15m2n – 27mn2

3.36k5 + 24k3 – 12k

4.4w3 + 3wz – 8w2 – 6w

5.x2 + 2x + x + 2

6.4m2 + 4mn + 3mn + 3n2

7.5p2 = 25p

8.(12a + 4)(3a – 1) = 0

9.b2 + 8b + 12

10.-4 – 3m + m2

11.–x2 + 8x – 15

12.p2 – 3p = 18

13.18x2 – 27x – 5

14.3x2 – 6y – 24y2

15.3x2 – 3x – 18

16.x2 – 49

17.-9 + p2

18.36 – 100w2

19.20x2 – 5y2

20.9x2 + 25y2

21.q2 – 14q + 36

22.4x2 – 8xy + 4y2

23.8x3 + 8

24.y6 - 1