Download Unit 1 - algebra2OHS

WARM UP
Multiply each Polynomial.
1. (x + 3)(x + 2)
3. 5(x + 3)
2. (x + 7)(x – 7)
4. (x + 7)(x – 4)
We are simplifying by using the _______________ property.
Unit 1: Rational Expressions
Lesson 1a:
Factoring and Simplifying
NC Goal 1.03:
Operate with algebraic expressions (polynomial,
rational, complex fractions) to solve problems
Performance Standards
TLW…
1. Find the Greatest Common Factor (GCF) of a polynomial.
2. Factor out a monomial from a polynomial.
3. Factor polynomials.
Essential Questions
1. How do you find the GCF of a polynomial?
2. How do you factor out a monomial from a polynomial?
3. How do you factor a polynomial with a coefficient = 1?
4. How do you factor a polynomial with a coefficient ≠ 1?
1. How do you find the GCF of a polynomial?
12x + 16 G.C.F. ______
15X3 – 20X2 G.C.F. _____
2. How do you factor out a monomial from a
polynomial?
4X3 – 12X2 + 16x
____(
)
1. Find the G.C.F. _______
2. Put the G.C.F. on the
outside of the
parenthesis
3. Divide coefficients from
original polynomial by
the G.C.F. and subtract
exponents
3. How do you factor a polynomial with a
coefficient = 1?
x2 - 13x + 30
1. Put the last term on top
2. Put the middle term on
the bottom
3. Find two numbers you
can multiply to get the
top number but add to
get the bottom number
4. Write your two factors
*If can’t be factored then it is prime
4. How do you factor a polynomial with a
coefficient ≠ 1?
2X2 + 11X +12
1. Multiply the coefficient of the first
term and the last term _____
2. Remove the leading coefficient
____ and rewrite the polynomial
using the new last term _____
3. Factor
4.
5.
You Try
1.-8X4 + 24X7 G.C.F. ___
2. 10x5 – 70X + 90 G.C.F. ___
Factor.
3. -2X2 – 10X + 14
4. 3x2y – 21xy
5. a2 + 4a+ 3
6. x2 - 3x - 18
7. 3c2 + 8c - 3
8. 2s2 – 13s - 24
Work Time Answers
1. (x + 2) (x + 3)
2. (y + 1)(y + 4)
3. (m + 5)(m + 7)
4. (p + 3)(p + 5)
5. (a + 2)(a + 6)
6. (n + 2)(n + 2)
7. (x + 3) ( x + 6)
8. prime
9. (y – 2)(y - 4)
10. (c – 3)(c – 5)
11. (m – 1)(m – 1)
12. (b – 4)(b – 5)
19. (7b – 2)(b – 2)
20. (3y + 5)(y – 2)
22. (2x – 1)(5x + 2)
21. (2c + 1)(3c + 4)
23. (4m -1)(3m – 2)
1. 4(x + 4)
2. 3y(y + 4)
3. 5x(2 + xy)
4. prime
5. 5r(3 + 4s)
6. 7a(2b + 3)
7. 3xy(3 – y)
8. 6mn(2m – 3n)
9. 2ab(4 + ab)
10. 4ab(4ac – 9b)
11. prime
12. 2xy(4xy2 -5)
Closure
Pre-Test Connections:
#s 1, 2, 3
Homework
Factor each of the Polynomials
1. x2 + 4x + 3
2. x2 – 4x – 21
3. x2 + 8x – 9
4. 2x2 + 5x + 3
5. 3x2 + 2x – 8
6. 3x2 – 6x – 24