Show complete solutions for full marks. 1. Using prime factorization, determine the least common multiple of 10, 12, 14 2. Using prime factorization, determine the greatest common factor of 54, 108, & 135. 3. Explain if 1728 is a perfect square using prime factorization.Use the following information to answer the next question. Josh wanted to expand and simplify the quadratic expression (5x+3)(2x-3). To find all terms in the multiplication process he used an area model as shown. 5x 2x 10x2 A - 3 B -9 4. State the terms represented by A and B.5. Expand and simplify the following: a) 5(4y+3)-3(7y-2) [2] b) (2x-9) c) 2(5x -2) (3x + 4) [2] 6. Determine the simplified expression for the area of the shaded region below: 5x 3x + 1 2x - 4 3x 7. Completely factor each of the following polynomials. a) 7a b' + 49ab [1] b) x- -1 1x + 28 c) y- -121 [1] d) 15x' - 42x + 248. Determine all of the positive values of I: for which 3:2 +12x+ k is factorahle over the integers. 9. Write each of the following mixed radicals as entire radicals. a) 4J h) llo 10. Write the followmg entire radicals as mixed radicals. a] Jsso h) {316 11. Without the use of a calculator, arrange the following from smallest to largest. add? 15 5J3 4J5 J5 12. Simplifyr the following expressions. Your nal answer should only contain positive exponents. a) (-113:2 y3 )3 (4x5 3:7 ) h) 4x2y3 4 8a]:5 13. Write the following expressions in radical form. Your final answer should only,r contain positive exponents. 3) {-3}? h) 1r; 14. Write the following expressions with the exponents in rational form. a) Jaw3 \"4