This document discusses expanding and factoring polynomial expressions. It introduces polynomials and the binomial expansion method of FOIL (First, Outer, Inner, Last). FOIL is used to expand expressions like (x + 4)2 into x2 + 8x + 16. The document also covers factoring polynomials by reversing the FOIL process. Factoring allows one to find the solutions to equations like x2 - 2x - 24 = 0, with solutions x = 6 and x = -4.
17. Factorization
x2 + 7x + 10
What are the clues?
Recall FOIL and reverse it.
18. Factorization
x2 + 7x + 10
F: the first term is the product of
the two first terms.
What gives us x2?
19. Factorization
x2 + 7x + 10
F: x and x
L: the last term is the product of
two terms.
What gives us 10?
20. Factorization
x2 + 7x + 10
F: x and x
L: 10 and 1, 5 and 2, -10 and -1,
OR -5 and -2.
OI: the middle term is the sum of
the outer and inner products.
What gives us 7?
21. Factorization
x2 + 7x + 10
F: x and x
L: 10 and 1, 5 and 2, -10 and -1,
OR -5 and -2.
OI: 5 and 2
So, our answer is (x + 5)(x +2).
22. Factorization
Use the FOIL method to check
your answer: (x + 5)(x + 2)
The result is x2 + 7x + 10 just as
it should be.
25. Factorization
x2 - 2x - 24
Use the clues:
L: What produces -24?
-24 and 1, -1 and 24, -12 and 2, -2
and 12, -8 and 3, -3 and 8, -6 and
4, OR -4 and 6