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Intermediate Algebra
- Indicate whether monomial, binomial, or trinomial, and state the degree:
3 xy^2 z^3
Type of polynomial _________
Degree of polynomial ________
- Add: 5 ) 3
( 5 x^3 7 x^2 3 x 4 )( 5 x^2 ^2 x
- Subtract:
) 2
( x^2 2 x x^2 x
- Multiply: ( 9 6 ) 3
(^2) x x (^2) x
- Multiply: 2 ( 5 x^2 7 y )^2 6. Multiply: [ 2 x ( 3 y 1 )][ 2 x ( 3 y 1 )]
- Multiply:
( 2 a 3 b )( 4 a^2 6 ab 9 b^2 )
- Divide:
3 2
4 3 3 2 2 4 3 12
xy z
xyz xyz xyz
- Divide using long division:
2 3
4 12 2 9 3 2
5 3 2
x
x x x x
- Divide using synthetic division:
3
2
6 4 5 3 7 2
x
x x x
- Factor. 3 2 7
(^3) x x
- Factor.
2 y^2 ( y 4 ) 3 ( y 4 )
- Factor.
8 x^2^ 4 xy 6 xy 3 y^2
- Factor. x^2 2 x 24
- Factor. 2 x^4 10 x^3 12 x^2
- Factor.
4 x^2 12 xy 9 y^2
- Factor. 6 x^2 7 x 3
- Factor. 9 x^4 45 x^2 14
- Factor. a^2 6 ab 9 b^2 36 c^2
- Solve for t. t^2 2 t 15
- Solve for a. 12 a^3 16 a^2 3 a
- Solve for x. 3 x^4 48 x^2 0
- Solve for r. 6 r^2 r 2
- Solve for k. ( k 7 )^2 k^2 ( k 1 )^2
- Find the area of the shaded region in factored form:
- Find the difference of the volumes of the two cubes in factored form:
x +
x + 4
7 x 7 x
7 x
4y
4y 4y
- Find the missing length by using the Pythagorean Theorem, a^2^ b^2 c^2 , and then factoring.
36. For f ( x ) 10 x^2 31 x 16 , find all the values of a for which f ( a ) 1.
- Find an equation whose graph will have the x - intercepts (5,0) and (-3,0).
- Find an equation whose graph will have the x - intercepts
1 and
^ , 0
x + 2
x +9 x +^11
- A rocket is projected upward from the top of a 144-foot-tall building with a velocity of 128 feet per second. The rocket’s distance from the ground, h , at any time, t in seconds, is given by the
formula h ( t ) 16 t^2 128 t 144.
a. Find the time it takes for the rocket to hit the ground.
b. Find the time it takes to be at a height of 256 feet.
- A ladder is leaning against a building. The distance of the ground between the base of the ladder to the building is 6 feet. The ladder reaches up the wall 2 feet less than the length of the ladder. Find the length of the ladder.
x feet
6 feet
