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Factoring Equations and Simplifying Expressions

1. Factor. 8m4n - 16mn4
A) 8m4n(1 - 16mn4)
B) 8m4n(1 - 2n3)
C) 8m4n4(m - 2n)
D) 8mn(m3 - 2n3)

2. Factor completely. b2 - ab - 6a2
A) (b - 3a)(b + 2a)
B) (b + 3a)(b - 2a)
C) (b - 6a)(b + a)
D) (b + 6a)(b - a)

3. Factor completely. 3(x - 2)2 - 3(x - 2) - 6
A) 3(x - 4)(x - 1)
B) 3(x - 4)(x + 1)
C) 3(x - 2)(x - 1)
D) 3(x - 2)(x + 1)

4. Factor completely. 12x3 - 3xy2
A) 12x(x - 3y)(x - y)
B) 3x(4x - y)(x + y)
C) 3x(2x + y)(2x - y)
D) 3x(2x - y)2

5. Factor by grouping. x3 - 5x2 + 2x - 10.

6. True or False? x2 - 18x + 81 = (x - 9)(x - 9)
A) True
B) False

7. State which method should be applied as the first step for factoring the polynomial.
2a2 + 9a + 10
A) Find the GCF.
B) Group the terms.
C) Factor the difference of squares.
D) Use the ac method (or trial and error).

8. Solve. x2 = -6x
A) 0, -6
B) 0, 6
C) 6, -6
D) 2, 6

1. Simplify. (b10)7

2. Evaluate (assume x  0).
6x0
A) 0
B) 1
C) 6
D) 6x

3. Add 5y - 4 and 2y2 - 8y.
A) 2y2 - 3y - 4
B) 2y2 + 3y - 4
C) 7y2 - 12y - 4
D) 2y2 + 13y - 4

4. Multiply. (-2a5b3)(5a4b)
A) 3a9b3
B) 3a20b3
C) -10a20b3
D) -10a9b4

5. Multiply. (4m - 3n)(4m + 3n)
A) 16m2 - 24mn + 9n2
B) 16m2 + 24mn - 9n2
C) 16m2 - 9n2
D) 16m2 + 9n2

6. Divide.

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Solution Summary

Equations are factored and expressions are simplified. The solution is detailed and well presented.

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