Math 0094
Review Test 3
Solutions
- Subtract the given polynomials:
- Add the following polynomials:
- Multiply the following polynomials:
(3x-8y)(4x + 2y) Use FOIL
- Multiply the following polynomials:
- Multiply
Rewrite as (3x 2)(3x 2) and then use FOIL:
- Divide
the following:
Divide each term in the numerator by the denominator:
- Divide
the following:
Rewrite as a long division problem: Put a zero in for any missing terms.
- Divide
the following:
- Simplify
the following:
:
Anything to the zero power is 1.
- Simplify
the following:
- Simplify
the following:
16x^4 y^12
- Put the following number in scientific notation. 93,000,000
9.3(10)^7
- Put the following number in scientific notation: 0.000 000 0037
3.7(10)^-9
- If the sun is 9.3(10^7) miles from the earth and light travels at 1.86(10)^5 miles per second, how long will it take light to reach the earth from the sun?
Distance = Rate x Time
=
= 5(10)^2
= 500 seconds or 8 minutes and 20 seconds
- Factor the following completely:
factor by grouping since there are 4 terms
Neither term factors further so we are done.
Factors
of 3 are 1 and 3. Factors of 24
are 1,24:
2,12: 3,8:4,6
Note that 3 cant pair with anything divisible by 3
such as 24, 12, 3, or 6.
(3x+2)(x-12)
Prime
GCF
difference
of two squares
9(3x + 1)(3x 1)
difference
of two cubes
The
sum of perfect cubes.
- Find all possible values of k for which the following will factor over the integers.
k=
(8x +1)(x-9) -71
(8x 1)(x + 9) 71
(8x + 9)(x 1) 1
(8x 9)(x + 1) -1
(8x + 3)(x 3) -21
(8x 3)(x +3) 21
(4x +1)(2x 9) -34
(4x-1)(2x + 9) 34
(4x + 9)(2x 1) 14
(4x 9)( 2x +1) -14
(4x+3)(2x-3) -6
(4x 3)(2x + 3) 6
The column on the right represents possible values of k.
- Use the area of rectangles to multiply (3x + 2)(2x +5)
6x^2 4x
3x +2
2x
+5
The product of the length and width is the area. This will be the sum of the 4 interior rectangles. Therefore (3x + 2)(2x +5) = 6x^2 + 4x + 15x +10 or 6x^2 +19x + 10.