Multiplying Polynomials Homework
Name:
Date:
Period:
Classify each by degree and term.
1. 4x3 – 2x
Cubic Binomial
2. 6x4 – 5x + 6
Quartic Trinomial
3. 5x2
Quadratic Monomial
4. 3x + 4
Linear Binomial
Find the Product: Write your answers in standard form.
A Monomial times a Polynomial
5. x(3x2 – 2x + 1)
6. -3m(m2 + 4m – 1)
3x3 – 2x2 + x
-3m3 – 12m2 + 3m
7. -3x5y3(4x2y + 5x3y8 – 3xy9)
8. 6x(6x3 – 3x + 1) – 5x(2x2 + 8x – 4)
-15x8y11 + 9x6y12 – 12x7y4
36x4 - 10x3 – 58x2 + 26x
A Binomial times a Binomial
9. (4x + 3)(2x – 4)
10. (-2x + 3)(9x + 5)
8x2 – 10x – 12
-18x2 + 17x + 15
11. (4x + 6)(4x – 6)
12. (x + 3)2
16x2 – 36
x2 + 6x + 9
A Binomial times a Trinomial
13. (2x – 4)(3x2 - 5x + 8)
14. (5x + 6)(4x3 - 2x - 3)
6x3 – 22x2 + 36x – 32
20x4 + 24x3 – 10x2 – 27x - 18
Find the Quotient: Write your answers in standard form.
15.
12𝑥 3 𝑦 8 −8𝑥 2 𝑦 5 +24𝑥𝑦 3 −36𝑦2
4𝑦 2
3x3y6 – 2x2y3 + 6xy – 9
16.
24𝑥 4 −30𝑥 3 + 18𝑥 2 −6𝑥
4x3 – 5x2 + 3x - 1
6𝑥
17. Allison has a rectangular garden. The length is four more than twice the
width. Write two expressions (in simplest form) that represent the perimeter
and area of the garden.
P = 2w + 2(2w + 4)
P = 6w + 8
A = (2w + 4) w
A = 2w2 + 4w
18. You have come up with a plan for building a wooden box to hold all of your
sports equipment as shown.
a. Write a polynomial expression (in simplest form) that represents the volume
of the box.
V = 24(3x + 6)(4x + 8)
V = (72x + 144)(4x + 8)
V = 288x2 + 1152x + 1152
b. Find the volume of the box when x = 10.
V = 41,472 in3
24 in
(3x + 6) in
(4x + 8) in