http://www.ck12.org Chapter 2. Polynomials and Rational Functions
- Show howa^3 +b^3 factors by checking the result given in the guidance section.
- Factor the following expression without using the quadratic formula or trial and error:
8 x^2 + 30 x+ 27
Answers: - Factoring,
a^3 −b^3 = (a−b)(a^2 +ab+b^2 )
=a^3 +a^2 b+ab^2 −a^2 b−ab^2 −b^3
=a^3 −b^3- Factoring,
a^3 +b^3 = (a+b)(a^2 −ab+b^2 )
=a^3 −a^2 b+ab^2 +ba^2 −ab^2 +b^3
=a^3 +b^3- Use the algorithm described in Example A.
8 x^2 + 30 x+ 27 →x^2 + 30 x+ 216
→(x+ 12 )(x+ 18 )
→(
x+^128)(
x+^188)
→
(
x+^32)(
x+^94)
→( 2 x+ 3 )( 4 x+ 9 )Practice
Factor each expression completely.
- 2x^2 − 5 x− 12
- 12x^2 + 5 x− 3
- 10x^2 + 13 x− 3
- 18x^2 + 9 x− 2
- 6x^2 + 7 x+ 2
- 8x^2 + 34 x+ 35
- 5x^2 + 23 x+ 12
- 12x^2 − 11 x+ 2
Expand the following expressions. What do you notice?
9.(a+b)(a^8 −a^7 b+a^6 b^2 −a^5 b^3 +a^4 b^4 −a^3 b^5 +a^2 b^6 −ab^7 +b^8 )