Download Hybrid Elementary Algebra 4.7 – 4.8 Introduction Division of

Hybrid Elementary Algebra
4.7 – 4.8 Introduction
Division of polynomials: Dividing by a monomial. To divide by a monomial, write each term of the
numerator over the monomial denominator and simplify.
16 x5 − 12 x3 + 20 x 2 + 6 x
1.
4x
=
16 x 5 12 x 3 20 x 2 6 x
−
+
+
4x
4x
4x
4x
= 4 x 4 − 3x 2 + 5 x +
3
2
9 x 2 + 3x − 6
2.
3
__________________
__________________
Division of polynomials: We use long division to divide by a polynomial.
3.
(x
2
+ 3 x − 18 ) ÷ ( x − 3)
x+6
x − 3 x + 3 x − 18
2
− ( x 2 − 3x )
6 x − 18
− ( 6 x − 18 )
0
Answer is x + 6 .
4.
(x
2
+ 11x + 24 ) ÷ ( x + 6 )
Hybrid Elementary Algebra
4.7 – 4.8 Introduction
Page 2 of 4
5.
(2x
3
t 2 − 13
6.
t−4
− 8 x − 7 ) ÷ ( x − 3)
2 x 2 + 6 x + 10
x − 3 2 x + 0 x2 − 8x − 7
3
−( 2 x3 − 6 x 2 )
6 x2 − 8x
− ( 6 x 2 − 18 x )
10 x − 7
−(10 x − 30 )
23
Answer is 2 x 2 + 6 x + 10 +
23
x −3
Scientific Notation
7. Write 4.83 × 10 4 in decimal notation.
8. Write 7.6 × 10−2 in decimal notation.
= 48300
9. Write 0.00923 in scientific notation.
= 9.23 × 10−3
10. Write 56,000,000 in scientific notation.
Hybrid Elementary Algebra
4.7 – 4.8 Introduction
Page 3 of 4
11. The average discharge at the mouth of the Amazon River is 4,200,000 cubic feet per second.
How much water is discharged from the Amazon River in one year?
First figure out how many seconds are in a year:
1 year
∗
365 days 24 hours 60 minutes 60 seconds
∗
∗
∗
= 31536000 seconds
1 year
1 day
1 hour
1 minute
Convert numbers to scientific notation to make computations more manageable.
4,200,000 cubic feet per second is 4.2 ×106 cubic feet per second.
31,536,000 seconds per year is 3.1536 × 107 seconds per year.
Now multiply, taking notice of the units.
So the discharge at the mouth of the Amazon is:
4.2 ×106 cubic feet 3.1536 ×107 seconds 13.24512 ×1013 cubic feet
∗
=
second
year
year
= 1.324512 ×1014 cubic feet per year.
12. An iPod hold 8 gigabytes of information. If a typical song is 3.5 megabytes, how many songs will
fit on the iPod? (Giga means billion or 109 and Mega means million or 106 )
Hybrid Elementary Algebra
4.7 – 4.8 Introduction
Page 4 of 4
Exponent Rules (again): Remember the exponent rules from last week. We now will see negative
exponent rules. Three additional exponent rules are useful when working with negative exponents.
−n
n
1
1
⎛a⎞
⎛b⎞
−n
n
Helpful Negative Exponent Rules:
a = n
=a
⎜ ⎟ =⎜ ⎟
a
a−n
⎝b⎠
⎝a⎠
Simplify each expression. Do not use negative exponents in your answer.
y4
y −3
13.
=y
14. t 2t −9
4 −( −3)
____________________
= y7
____________________
⎛ 5a 4 ⎞
15. ⎜
⎟
⎝ 3 ⎠
⎛ 3 ⎞
=⎜ 4 ⎟
⎝ 5a ⎠
=
=
−2
16.
2
____________________
32
52 ( a 4 )
____________________
2
9
25a8
17.
( 5x
8 a −6
2a −10
____________________
−1
y
)
2 −2
⎛ 3x −4 ⎞
⎟
18. ⎜
⎝ 9x ⎠
3