### Factoring Polynomials

Factor completely: 27z^3-125

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Factor completely: 27z^3-125

Find the greatest common factor of the two expressions 10 t y z and 25 y^2 z^8 Simplify the answer as much as possible.

Factor completely: 2 t^4 x^4 - 2 x^4

Find the value of k such that x^2 - 18x + k is a perfect square.

Evaluate the following two expressions. Write the answer without exponents. a) 16 ^ - 3/2 b) ( 1/8) ^ 4/3

Simplify the following: x^2 z^6 ----------- x^4 z^3

Write in simplified radical form by rationalizing the denominator -2 sqrt 2 + 2 ----------------- -3 sqrt 2+ 5

Bring the following down to the simplest expression possible: sqrt (27/12)

The following radical should be simplified: 5 sqrt(20) + sqrt(80)

Reduce the following rational expression to its lowest terms: 9 u^4 w^4 --------------------- 9 w z^6 + 6 w^3

Write 2 d^3 y^3 t ------------- - ----------- 9ak 3a^3 d as a single rational expression.

Find the roots of the quadratic equation: z^2 + 9z + 20 =0 (If there is more than one root, separate them with commas.)

Factor 10u+ yz + uy + 10z

Factor 2x^2 - 11x +14

Factor completely: 30 u^6 + 65 u^5- 25 u^4

(6w + 2t - 3) (5w + 6t - 3) Simplify the answer as much as possible

Simplify: Write your answer without using negative exponents. 4z^7 w^-9 * 8 x *3 z^-7 x^7 w^6

A) Given the function z = x3 - 6xy +y3, find and classify the stationary points. b) Show that the minimum surface area of a rectangular box (which has a top), of volume 8 cubic meters, is equal to 24 square meters.

Julia wants to have a small but productive orchard. Experienced farmers have told her that if she plants 20 trees, she will get 24 bushels of fruit from each tree. But every additional tree she plants will cause crowding and result in an orchard-wide drop in yield of 1 bushel per tree. How many trees should she plant to get t

Solve for z: (z - 5)^2 = 2z^2 - 11z + 5. Make sure to provide all of the required steps.

Solve 5 u^2 - 13u + 6 = 0. (If there is more than one solution, separate them with commas.)

Solve for z: sqrt 8z + 8 = sqrt 6z + 11 Please help me with this and thanks for your help in advance!

Simplify: sqrt (27/48) Be sure to write the answer in lowest terms

Please simplify the following radical: 5 sqrt(45) + sqrt(80)

Write the following: 5au 4x^2 --------------- + ----------- 9d^2 k^2 3a^2 k as a single rational expression

Express the following sum as a single fraction: 3x + t 7x + 5t - ------------ + ------------- 2x 2x Reduce the result to lowest terms whenever possible

Factor: wu - 2y -2u + yw

Write without parentheses ( u^4) ^2 ------ (-2 w^3) NOTE: There should only be one parentheses. I couldn't figure out how to enclose the problem in one..so I included two.

Solve x^2 = -2 where x is a real number. Simplify your answer as much as possible. (If there is more than one solution, separate them with commas.)

(3-2√7)(3+2√7)