Http://. Basic Polynomial Operations Simplify each expression 1.2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12

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Basic Polynomial OperationsSimplify each expression

1. 2.

3. 4.

5.

6. 7. 8.

9. 10.

11. 12.

(5a−2b+ 4) + (2a−5b−6) (4a2 −5ab−6b2 ) + (10ab−6a2 −b2 )

(3x2 −2x+ 5y2 )−(−2x2 + 5x−2y2 )(7a−3b−8)−(3−4a+ 5b)

(2x2 + 3x+ 2) + (4x−5)−(−7x2 + 8)

(x−8)2 (5x−2)2 (2x + 9)(2x−9)

(2x + 5)(4x−3) (4x−3y)(5x+ 2y)

3(2x−3)2 −2(x − 2)3

Monomials/ExponentsSimplify each expression1. A. B. C.

1. A. B. C.

2. A. B. C.

Challenge Problems4. Find the value of r. A. B.

4y2 ∗5y3 5y4 (−2y)5 17a3b2 (−2a4 )(−3b)

−5z(3y + 4z) 9y2 (7y2 + 5y−3)−12c(6c2 + 8c − 4)

6x3y2z4

3xyz

−15m−2

5m−6

(2xy2 )3

4x2y4

x24 =x4r

xr x15 =x2r ∗xr

Monomials/ExponentsMultiply 1. A. (4x)2 B. (2a2b)(4ab2) C. (4pq)(-2p2q3) D. (-5x2y3)(7xy4)(2xy)

2. A. B.

Multiply, then add or subtract.1. A. B.

C. D.

(2x)2 (xy2 )3(3xz2 )2 (3a3b)(5a2b2 )2 (2ab)2

(2x2ab)2 (2a2b2 )−(abx)3(3abx) (2up2 )(4up)3 −(3u4p)(9p4 )

(−2nm)(3nm)3 −(−8mn)2 (mn)2 (−3ab)2 (3ab3)−(5b)2 (−10ab)3

Factoring

1. What is the Greatest Common Factor (GCF) :A. 28, 49 B. 48, 72, 96 C. 15xy, 45x2, 60x2y2

2. Factor, write prime if it does not factor.(use greatest monomial factor method)A. 12a3b + 15ab2 B. 24x2 – 8x C. 18m2n4 - 12m2n3 + 24m2n2

(use difference of square method)D. x2 – 1 E. 9y2 – 16 F. 4a2 – 81b2

(use grouping method)G. n2 + 2n + 3mn + 6m H. 6ax – 3a + 4bx -2b

Factoring

3. Factor each trinomial, write prime if it does not factor.A. B.

C. D.

E. F.

G. H.

I. J.

x2 + 6x+ 8 y2 −x−6

m2 +13m−36 x2 −22x−75

x2 −11xy−60y2 x2 + 8xy+12y2

3x2 + 21xy−54y2 2x2 −5x−3

5a2 −42a−27 6x2 −7x−20

Solving equations using FactoringFind the solution: 1. put in standard form (set to zero) 2. factor completely 3. set each part to zero 4. solve for the variable.

Identify the vertex and graph with using a graphing calculator.

A. B.

C. D.

E. F.

CHALLENGE PROBLEMS!!!!!G. H.

x2 −7x=−12 x2 + 9 =10x

y2 −49 =0 6x2 −16x+ 8 =0

n2 −16n=0 3x2 −2 =x2 + 6

v3 =10v−3v2 x5 −16x=0

Solve using complete the square method or the Quadratic Formula.

Find the real zeros (x-intecepts/solutions) and vertex using Complete the square method.

1. 2.

3. 4.

Find the real zeros using the quadratic formula.5. 6.

7. 8.

y =2x2 −4x+ 8 y =−3x2 −12x−13

y =13x2 −2x+ 3 y =5x2 + 40x+ 77

y =2x2 +12x+17 y =6x2 −7x−20

y−5 =−8(x−6)2 y + 8 =3(x+1)2

Solving quadratic word problems1. A square field had 9cm added to its length and 3cm added to the width. Its new

area is 280cm2. Find the length of the original field.

2. The perimeter of a rectangular piece of property is 8 miles and its area is 3square miles. Find the dimensions.

3. The area of a rectangular pool is 192 square meters. The length of the pool is 4meters more than its width. Find the length and width.

4. Fourteen less than the square of a number is the same as five times the number. Find the number.

5. The sum of the squares of two consecutive positive even integers is 340. Find the integers.

6. Challenge: The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers. Find the five integers.