1. Adding and Subtracting Polynomials
ALGEBRA 1 LESSON 9-1
Simplify each expression. Then name each polynomial by its degree and number of terms.
1. –4 + 3x – 2x2
2. 2b2 – 4b3 + 6
3. (2x4 + 3x – 4) + (–3x x4)
4. (–3r + 4r2 – 3) – (4r2 + 6r – 2)
–2x2 + 3x – 4; quadratic trinomial
–4b3 + 2b2 + 6; cubic trinomial
3x4; fourth degree monomial
–9r – 1; linear binomial
9-1

2. Multiplying and Factoring
ALGEBRA 1 LESSON 9-2
1. Simplify –2x2(–3x2 + 2x + 8).
2. Find the GCF of 16b4 – 4b3 + 8b2.
3. Factor 3x3 + 9x2.
4. Factor 10y3 + 5y2 – 15y.
6x4 – 4x3 – 16x2
4b2
3x2(x + 3)
5y(2y + 3)(y – 1)
9-2

3. Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Simplify each product using any method.
1. (x + 3)(x – 6) 2. (2b – 4)(3b – 5)
3. (3x – 4)(3x2 + x + 2)
4. Find the area of the shaded region.
x2 – 3x – 18
6b2 – 22b + 20
9x3 – 9x2 + 2x – 8
2x2 + 3x – 1
9-3

4. Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Find each square.
1. (y + 9)2 2. (2h – 7)2
5. Find (p3 – 7)(p3 + 7). 6. Find 32 • 28.
y2 + 18y + 81
4h2 – 28h + 49
1681
841
p6 – 49
896
9-4

5. Factoring Trinomials of the Type x2 + bx + c
ALGEBRA 1 LESSON 9-5
Factor each expression.
1. c2 + 6c x2 – 11x g2 – 2g – 24
4. y2 + y – m2 – 2mn + n2
(c + 3)(c + 3)
(x – 2)(x – 9)
(g – 6)(g + 4)
(y + 11)(y – 10)
(m – n)(m – n)
9-5

6. Factoring Trinomials of the Type ax2 + bx + c
ALGEBRA 1 LESSON 9-6
Factor each expression.
1. 3x2 – 14x + 11
2. 6t2 + 13t – 63
3. 9y2 – 48y – 36
(x – 1)(3x – 11)
(2t + 9)(3t – 7)
3(3y + 2)(y – 6)
9-6

7. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Factor each expression.
1. y2 – 18y a2 – 24a + 16
3. p2 – x2 – 225
5. 5m2 – c2 + 20c + 50
(y – 9)2
(3a – 4)2
(p + 13)(p – 13)
(6x + 15)(6x – 15)
5(m + 3)(m – 3)
2(c + 5)2
9-7

8. Factor each expression. 1. 10p3 – 25p2 + 4p – 10
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
Factor each expression.
1. 10p3 – 25p2 + 4p – 10
2. 36x4 – 48x3 + 9x2 – 12x
3. 16a3 – 24a2 + 12a – 18
(5p2 + 2)(2p – 5)
3x(4x2 + 1)(3x – 4)
2(4a2 + 3)(2a – 3)
9-8