^g r Practice and Problem-Solving Exercises
PracticeMATHEMATICAL
PRACTICES^ ApplySimplify each product.- 7x(x + 4)
- -w 2{w - 15)
- (b + U )2 b
- 4x(2x3 - 7x2 + x)
Find the GCF of the terms of each polynomial.- 12x+20 16. 8w2 — 1 8 u?
- a3 + 6a2 - 11a 19. 4 x 3 + 12x - 28
Factor each polynomial.- 9x — 6
- 5k3 + 20k2- 15
22. t2 + 8 1- 14x3 - 2x2 + 8x
11. 3m2(10 + m) - -8 y 3(7y2- 4 y - l)
See Problem 2.- 451? + 2 7
- 14z4 - 4 2 z 3 + 2 1 z 2
See Problem 3.- 14n3 - 35n2 + 28
- g4 + 24g3 + 12g2 + 4g
See Problem 1.- Art A circular m irror is s u rro u n d e d by a square m etal frame. The radius of the See Problem 4,
m irror is 5x. The side length of th e m etal fram e is 15x. W hat is th e area of th e m etal
fram e? W rite your answ er in factored form. - Design A circular table is p ain ted yellow w ith a red square in th e m iddle. The
radius of th e tabletop is 6x. The side length of th e red square is 3x. W hat is the
area of th e yellow p a rt of th e tabletop? W rite your answ er in factored form.
Simplify. Write in standard form.- —2x(5x2 - 4x + 13) 30. -5y2(-3y3 + 8y)
- pip + 2) - 3pip - 5) 33. t\ t + 1) - t{2t2 - 1)
6 x- 10a(-6a2 + 2a - 7)
- 3c(4c2 - 5) - c(9c)
3 5. T h in k A b o u t a Plan A rectangular w o o d en fram e h as side lengths 5x an d 7x + 1.
The rectangular opening for a picture has side lengths 3x an d 5x. W hat is the area of
th e w ooden p a rt of th e fram e? W rite your answ er in factored form.- How can draw ing a diagram help you solve th e problem?
- How can you express th e area of th e w o o d en p a rt of th e fram e as a difference
of areas?
3 6. E rro r A n alysis D escribe a n d correct th e error m ad e
in multiplying.
Factor each polynomial.- 17xy4 + 51x2y 3 38. 9 m4n5 — 27m2n3 39. 31a6b3 + 63a5
- a. Factor n2 + n.
b. W riting Suppose n is a n integer. Is n2 + n always, sometimes, or never a n e v e n
integer? Justify your answer.
c
PowerAIgebra.com Lesso n 8-2 Multiplying and Factoring 495