Math homework help?

Question

Section 10.5: Let's look at problems #67 [x^3 + x^2 + x + 1)(x - 1)]and #68 [(x + 2)(x^3 - x^2 + x - 2)]. These problems are very long, so be sure to take turns within each problem, and explain step-by-step how to perform the multiplication, and how to simplify the resulting monster polynomial.

Answer 1

x(x^3+x^2+x+1)-1(x^3+x^2+x+1)
=x^4+x^3+x^2+x-x^3-x^2-x-1
x^4+x=x(x^3+1)
(x+2)(x^3-x^2+x-2)
=x(x^3-X^2+x-2)+2(x^3-x^2+x-2)
x^4-x^3+x^2-2x+2x^3-2x^2+2x-4)
x^4+x^3-x^2-4

Answer 2

It's all about the distributive property.

In problem "67, you are going to distribute two times. Take x and distribute to x^3+x^2+x+1, then take the -1 and distribute to x^3+x^2+x+1. Once you have multiplied all of those terms out. See if you have any like terms to combine.

Hope this helps. Good Luck

Answer 3

#67 (x^3+x^2+x+1)(x-1)
x^4+x^3+x^2+x-x^3-x^2-x-1
X^3 and X^2 and X cancel out so=
x^4-1 is the answer

#68 (x+2)(x^3-x^2+x-2)
x^4-x^3+x^2-2x+2x^3-2x^2+2x
x^4+x^3+x^2 is the answer

Answer 4

#67 [x^3 + x^2 + x + 1)(x - 1)

Write in the format: One polynomial below the other one. Like

x^3 + x^2 + x + 1
Multiply by x - 1
-------------------------------------------
x^4 + x^3 + x^2 + x (Mulitiplication by x alone)
- x^3 - x^2 - x - 1 (Mulitiplication by - 1)
-------------------------------------------
x^4 0 0 0 - 1 (By adding)

i.e x^4 - 1
=====

Exactly In the same manner
#68 [(x + 2)(x^3 - x^2 + x - 2)]

will give you:

x^4 - x^3 + x^2 - 2x
2x^3 - 2x^2 + 2x - 4
-------------------------------------------
x^4 + x^3 - x^2 0 - 4 or

x^4 + x^3 - x^2 - 4
==============

Answer 5

for each expression, multiply the first term by the first, then add to it the first times the second, then first times third, etc. THEN multiply the 2nd term by the 1st, 2nd by 2nd, etc. then add all the terms together keeping the powers in correct order. SO
x^4 + x -1 and x^4 + x^3 - x^2 -4.

Answer 6

#68 same thing as 67 multiply the x by everything first and then the number and then combine any like terms.