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.
Ans: 2 x^2 – 9x
2. Add:
3p2 – 5p – 4 and 9p2 + 10p – 2
Ans: 12 P^2 + 5p - 6
3. Is the algebraic expression a polynomial? If so, give its degree.
9x3 + 6x6 + 8
Ans: Yes. The degree is 6.
4. Perform the indicated operations and simplify.
5x – 4x[8 – 3(x – 2)]
Ans: 12 x^2 – 51x
5. Multiply and simplify.
(3x – 1)(2x + 5)
Ans: 6 x^2 + 13x - 5
6. Multiply and simplify:
(5x – 3y)2
Ans: 25 x^2 - 30xy + 9 y^2
7. Multiply and simplify:
(3x2 – 2x – 1)(x2 + x + 5)
Ans: 3x^4 + x^3 + 12x^2 – 11x - 5
8. Subtract 4x2 – 5x from the sum of 9x2 – 2 and 6x – 1.
Ans: 5x^2 + 11x - 3
9. Factor completely relative to the integers.
x2 – 8x + x – 8
Ans (x-8)(x+1)
10. Factor completely relative to the integers.
25x2 – 5x – 2
Ans: (5x-2)(5x+1)
11. Factor completely relative to the integers.
49a2b – b3
Ans: b (7a + b) (7a - b)
12. Factor completely relative to the integers.
8a3 + 27
Ans (2a + 3)(4a^2 – 6a +9)
13. Reduce to lowest terms.
Ans: (x - 8)
14. Subtract and reduce to the lowest terms:
2/4 - 1/6
Ans: 1/3
15. Perform the indicated operations and reduce to lowest terms.
Ans: a b^2
16. Divide and reduce to lowest terms.
Ans: (x-3)(x+5)
17. Factor completely relative to the integers.
x2 + 36
Cannot be factorized.
If the question is x^2 – 36 , then the answer is (x+6)(x-6).
18. Reduce to lowest terms:
18/54
Ans: 1/3
19. Factor completely relative to the integers:
16x2 + 40x + 25
Ans: (4x+5)(4x+5) or (4x+5)^2
20. Factor out, relative to the integers, all factors common to all terms.
49x4 – 70x3 + 21x2
Ans: 7x^2 (x-1) (7x-1)