# Algebra: Mix of Simplification & Factorization problems

1. Multiply (2-5x⁷)² =_____

2. The base of a triangle is 4 cm greater than the height. The area is 30 cm². Find the height and length of the base.

Height is ________cm

Base is _________cm

3. (y²-7) (6y²-3y+5) =_______

4. Find the greatest common factor (GCF) of 12x and 14x³ The GCF is_____________

5. Solve w² = 25

A. The solution is_______

B. There is no solution.

6. The number N, in millions, of hearing impaired people of age x can be approximated by

N = -0.00006x³ + 0.006x² -0.1x + 1.5. Approximate to the nearest million the number of hearing impaired people of age 25 and 35.

N = ________million people of age 25 (round to the nearest million as needed)

N =_________million people of age 35 (round to the nearest million as needed)

7. Simplify (7⁸) -⁵ =_____

8. Divide (16x³ -34x² -71 x -21) (8x + 3)=________

9. Factor the trinomial r² + 9r +20 =______

10. Subtract (xy - ab -8) -(xy - 8ab -1) =_________

11. 14x⁸ -42x⁷ + 35x³ _____________ = _______

-7x³

12. Suppose it takes 3 days for a space vehicle to travel from earth to the moon. About how long would it take the same vehicle traveling at the same speed to reach Venus? Closest distance from earth to : moon: 240,000 mi Venus: 26,000,000 mi

The space vehicle would take about _________days to reach venus. (round to the nearest whole number. Use scientific notation.)

13 Simplify (4m⁴)³ =_______

14 For the polynomial, -3x⁴ +7x³ -4x² +5x -1, complete the table

Term coefficient degree of the term degree of the polynomial

____ ______ ________

7x³ 7 ________

____ ______ 2

5x ______ 1

-1 ______ _______

15 Solve c² -14c +45 =0

A. The solution is_____

B. There is no solution

16 Simplify

A. 3² =____

B. 3-² =______

C. ( 1/3)² =______

D. (1/3)-²=_____

E. -3²=______

F. (-3)²=______

17 Convert to decimal notation. 10-⁴=______

18 factor completely v² +36 -12v =_____

19 evaluate n² -8 when n=-11. n² -8=_____

20 collect like terms. 7x -9x =_____ -

21 factor. 4x² +32x

22 divide and check answer

30x⁴ y² ________

6x ^6 y²

23 multiply and simplify ( 3h )^6 x (3h)³ =______

24 factor 3s⁵-192s² =_____

25 add (8x² -7x +25) + (7x² + 9x -48) =______

27 multiply (x = 3) (x - 3)=_______

28 divide and simply 3^19/3^5 =______

31 multiply (9x² +4) (9x² -4) =_______

32 subtract (1/10x³ -1/4x -1/9) -(-1/10x³ +1/4x -1/9) =________

33 Add (r -3s +1)+(4r + 2s) + (s +1)=________

34 multiply (-1/6x⁵) (-1/5x)=_______

36 express using a positive exponent 1/z^-3=_____

37 Factor by grouping 6x^3 -6x^2 - x + 1=________

#### Solution Summary

The solution provides step by step method for the multiplication, subtraction division, and factorization of algebraic expressions. Formula for the calculation is also included.