1. The width of a rectangle is 9 inches less than 2 times the length. If x repre

Question

1. The width of a rectangle is 9 inches less than 2 times the length. If x represents the length, write an algebraic expression in terms of x that represents the area of the rectangle. Simplify the expression.

2. Add:

3p2 – 5p – 4 and 9p2 + 10p – 2


3. Is the algebraic expression a polynomial? If so, give its degree.

9x3 + 6x6 + 8




4. Perform the indicated operations and simplify.

5x – 4x[8 – 3(x – 2)]


5. Multiply and simplify.

(3x – 1)(2x + 5)

6. Multiply and simplify:

(5x – 3y)2

7. Multiply and simplify:

(3x2 – 2x – 1)(x2 + x + 5)

8. Subtract 4x2 – 5x from the sum of 9x2 – 2 and 6x – 1.

9. Factor completely relative to the integers.

x2 – 8x + x – 8

10. Factor completely relative to the integers.
25x2 – 5x – 2

11. Factor completely relative to the integers.

49a2b – b3


12. Factor completely relative to the integers.

8a3 + 27


13. Subtract and reduce to the lowest terms:

2/4 - 1/6




14. Factor completely relative to the integers.

x2 + 36


15. Reduce to lowest terms:

18/54


16. Factor completely relative to the integers:

16x2 + 40x + 25


17. Factor out, relative to the integers, all factors common to all terms.

49x4 – 70x3 + 21x2

Explanation / Answer

1.w=2l-9
2. 12p2+5p-6
3. yes, degree 6.
4. 5x – 4x[8 – 3(x – 2)] =5x – 4x[8 + (-3)(x – 2)] = 5x – 4x[8 – 3x + 6] = 5x – 4x[14 – 3x] = 5x + (-4x)[14 – 3x] = 5x -56 +12x2 = 12x2+5x-56

5. (3x – 1)(2x + 5) = 6x2-2x+15x-5 = 6x2+13x-5

6. (5x – 3y)2=(5x – 3y)(5x – 3y) = 25x2-15y-15y+9y2= 25x2-30y+9y2

7. (3x2 – 2x – 1)(x2 + x + 5) = 3x4-2x3-x2+3x3-2x2-x+15x2-10x-5 = 3x4+x3+12x2-11x-5

8. (9x2 – 2)+(6x – 1)-(4x2 – 5x) = 9x2-2+6x-1-4x2+5x = 5x2+11x-3

9. x2 – 8x + x – 8 = x(x – 8) + 1(x – 8) = (x-8)(x+1)
10. 25x2 – 5x – 2 = (5x-2)(5x+1)
11. 49a2b – b3= b(49a2 – b2) = b(7a+b)(7a-b)

12. 8a3 + 27 = (2a+3)(4a2-6a+9)

13. 2/4 - 1/6 = (3*2)/(3*4) - (2*1)/(2*6) = 6/12 - 2/12 = (6-2)/12 = 4/12 = (4*1)/(4*3) = 1/3
14. x2 + 36 IMPOSSIBLE TO FACTOR, UNLESS YOU ARE USING IMAGINARY NUMBERS, IN WHICH CASE, THE FACTORED FORM IS: (x-6 i) (x+6 i)

15. 18/54 = (2*3*3)/(2*3*3*3) = 1/3
16. 16x2 + 40x + 25 = (4x+5)(4x+5) = (4x+5)2
17. 49x4 – 70x3 + 21x2=7x2(7x2-10x+3) = 7x2(7x-3)(x-1)

RATE THIS LIFESAVER SINCE I ANSWERED THEM ALL.

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