CHOOSING A FACTORING METHOD WORKSHEET

Problem 1 : 

2y(y² + 4)

Problem 2 : 

(2x + 6)(x + 5)

Problem 3 :

Factor -2xy² + 16xy - 32x completely. Check your answer.

Problem 4 :

2x² + 5x + 4

Problem 5 :

3n⁴ - 15n³ + 12n²

Problem 6 :

4x³ + 18x² + 20x

Problem 7 :

p⁵ - p.

Problem 8 : 

x⁶ - 7y²

Detailed Answer Key

1. Answer :

2y(y² + 4)

Neither 2y nor y² + 4 can be factored further.

2y(y² + 4) is completely factored. 

2. Answer :

(2x + 6)(x + 5)

2x + 6 can be further factored.

Factor out 2, the GCF of 2x and 6.

=  2(x + 3)(x + 5)

2(x + 3)(x + 5) is completely factored.

3. Answer :

-2xy² + 16xy - 32x

Factor out the GCF.

=  -2x(y² - 8y + 16)

y² + 8y + 16 is a perfect square trinomial of the form

a² + 2ab + b²

a = y and b = 4.

=  -2x(y - 4)²

Check : 

-2x(y - 4)²  =  -2x(y² - 8y + 16)

=  -2xy² + 16xy - 32x ✓

4. Answer : 

2x² + 5x + 4

The GCF is 1 and there is no pattern.

=  ( _ x + _ ) ( _ x + _ )

a = 2 and c = 4; Outer + Inner = 5. 

2x² + 5x + 4 is unfactorable.

5. Answer : 

3n⁴ - 15n³ + 12n²

Factor out the GCF.

=  3n²(n² - 5n + 4)

There is no pattern.

=  3n²( n + _ ) (n + _ )

b = -5 and c = 4; look for factors of 4 whose sum is -5.

The factors needed are -1 and -4.

=  3n²(n - 1)(n - 4)

6. Answer : 

4x³ + 18x² + 20x

Factor out the GCF.

=  2x(2x² + 9x + 10)

There is no pattern.

=  2x( _ x + _ ) ( _ x + _ )

a = 2 and c = 10; Outer + Inner = 9

=  2x(x + 2)(2x + 5)

7. Answer : 

p⁵ - p

Factor out the GCF.

=  p(p⁴ - 1)

p⁴ - 1 is a difference of two squares.

=  p(p² + 1) (p² - 1)

p² - 1 is a difference of two squares.

=  p(p² + 1) (p + 1)(p - 1)

8. Answer : 

x⁶ - 7y²

7y² is not a perfect square.

x⁶ - 7y² is not the difference of two squares because 7y² is not a perfect square.

x⁶ - 7y² is unfactorable.

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