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+ 2y

Simplify the polynomial and write it in standard form. − 3a − 2 + a 2 − 4a + 6 + 5a 2. 1. = 6a 2. − 7a. + 4. Find the sum or difference. A. (3x 2 − 8x + 2) + ( x 2 + 5x − 3). 1. = 4x 2. − 3x. − 1. B. (5x − 6y) + (2x + 8y). = 7x. + 2y. C. = − 6 x 2. + 14.

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  1. Simplify the polynomial and write it in standard form. −3a − 2 + a2− 4a + 6 + 5a2 1 = 6a2 −7a + 4 Find the sum or difference. A. (3x2 − 8x + 2) + ( x2+ 5x − 3) 1 = 4x2 − 3x − 1 B. (5x − 6y) + (2x + 8y) = 7x + 2y C. = −6x2 + 14 (2x2 + 5) −(8x2 − 9) +− = (2x2 + 5) + (−8x2 + 9) (9n2− 3n) − (3n2 − 5n + 4) +− = 6n2 + 2n − 4 D. (9n2− 3n) + (−3n2+ 5n − 4)

  2. Simplify: B. −4a2 ( 2a2 ─ 3a) +− A.(3x2y4)(2x3y5) (−4a2) ∙ 2a2 + (−4a2)∙ (−3a ) 1 3 ∙ 2 ∙ x2+3 ∙ y4+5 = −8a4 + 12a3 = 6 x5y9 D. (x + 3)2 C. (x + 3)(x + 3) + 3x + 3x + 9 x2 x2 +6x + 9 D. (2y − 2)(y2 − 3y + 4) 2y − 2 2y∙ y2 + 2y∙(−3y) + 2y∙4 + (−2) ∙ y2 + (−2)(−3y) + (−2) ∙ 4 2y3 + (−6y2) + 8y + (−2y2) + 6y + (−8) 2y3 − 8y2 + 14y − 8

  3. 6a3 − 15a2 + 9a −3a 6a3 −15a2 9a = + + −3a −3a −3a = −2a2 + 5a + − 3 − Simplify: Write the answers using positive exponents. B. −22x−3∙ x0 C. A. (−2x3y2)2 (−2)2∙x3∙2∙y2∙2 = −5a5−2∙b2−3 =−5a3b−1 D.

  4. Simplify: Write the answers using positive exponents. C. A. B. D. Write 6,031,000 in Scientific Notation: 6.031 x 106 E. Change 4.2 x 10−3 into decimal form: 0.0042

  5. A. Give the greatest common factor of the monomials: B. Factor Completely: 18x3y2, 30x2y5 27a3b2− 12ab2 3ab2(9a2− 4) GCF: 6x2y2 3ab2(3a + 2)(3a − 2) C. Factor: D. Factor: E. Factor: x2 − 25 (x + 5)(x −5) (x + 1)(x −4) (x + 2)(x + 6) F. Factor Completely: 2x3 +6x2 − 8x 2x(x2 +3x− 4) 2x(x+4)(x− 1)

  6. Solve: Solve: A. x2 + 5x − 24 = 0 B. 2x2 − 2x − 12 = 0 (x − 3)(x + 8) = 0 2(x2− x − 6) = 0 x − 3 = 0 or x + 8 = 0 2(x + 2)(x −3) = 0 x = 3 or x = −8 x + 2 = 0 or x − 3 = 0 Sol. Set: {−8, 3} x = −2 or x = 3 Sol. Set: {−2, 3} Solve by completing the square: C. x2 − 6x = 1

  7. Simplify: B. A. Solve: ] [ D. 6 ∙ C. 10x ∙ 20 − 2x = 4 −2x = −16 x = 8

  8. Simplify: C. B. A. Solve: E. D. ] [ ∙ (x+5)(x−5) 2∙(x+5) = 4 2 x + 10 = 4 2 x = −6 x = −3

  9. A. What is the sales price of a $40 sweater that is on sale for 33% off? 33% of $40 = $40 − $13.20 = $26.80 .33 ∙ $40 = $13.20 $26.80 sales price B. 30 is 125% of what number. 30 = 1.25 ∙ n n = 24 C. The height of a triangle is 3 cm more than its base. If the area of the triangle is 90 cm2, write an equation that can be used to find the measure of the base, b and solve for b. b = 12 cm

  10. 13 ft ? √ √ 5 ft The top of a 13 ft ladder is propped against the side of a house. The bottom of the ladder is 5 feet from the house. How far up the wall does the top of the ladder touch the house? a2 + b2 = c2 52 + b2 = 132 c= = b 25 + b2 = 169 a= b2 = 144 b = 12 ft

  11. Simplify: D. C. B. A. F. E. G. Rationalize and simplify:

  12. √ √ Solve: C. (x + 4)2 = 16 x + 4 = ±4 x − 1 = 100 x + 4 = 4 or x + 4 = −4 x = 101 x = 0 or x = −8 D. 6n2 − 150 = 0 6n2 = 150 n2 = 25 n = 5, −5 3x + 1 = 100 3x = 99 x = 33

  13. x1 + x2 4 + 2 5+ 7 y1 + y2 ( ) ( ) 2 2 2 2 , , x A. Find the distance between the points A(1, 1) and B(3, 4) x2 = 22 + 32 x 3 2 B. Find the midpoint of the segment with the following endpoints: (4, 5) and (2, 7). midpoint: = (3, 6)

  14. Solve using the quadratic formula: ax2 +bx + c = 0 x2 −3x −7 = 0 a = 1, b = −3, and c = −7

  15. Use the discriminant to find the number of real number roots of this equation: ax2 +bx + c = 0 Discriminant: b2 − 4ac 5x2 +10x + 5 = 0 = 102 − 4∙5∙5 a = 5, b = 10, and c = 5 = 100 − 100 = 0 The discriminant is equal to “0” so there is one real number root.

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