# Factoring the polynomial

Please see the attached file for the complete list of problems (25 in all)

1. Find the greatest common factor for the following sets of terms. 12a^3b^2 , 18a ^2b^3, 6a^4b^4

2. Factor the following polynomial. 4s + 6st - 14st ^4

3. Find the GCF of (6y^2 - 3y)(y + 7)

4. Geometry: The area of a rectangle of length x is given by 3x^2 + 5x. Find the width of the rectangle.

5. Factor the follosing trinomial completely: x^2 - 11x - 60

6. Factor the following trinomial completely: 2a^3 - 52a^2b +96ab^2

7. Find all positive values for k for which the following can be factored: x^2 +x - k

8. Factor the following polynomial completely: 14x^2 - 20x + 6

9. Factor the following polynomial completely: -3s^2 - 10s + 8

10. Factor the following binomial: 25x^2 - 81y^2

11. Determine whether the following trinomial is a perfect square. If it is, factor the trinomial: x^2 - 24x + 48

12. Factor the following trinomial: 16x^2 + 40xy + 25y^2

13. Factor the following expression: a^2(b-c) - 16b^2(b-c)

14. Factor the following expression:

15. Factor the following polynomial by grouping the first two terms and the last two terms. x^3 - 4^2 +2x - 8

16. Factor the following polynomial completely by factoring out any common factors and then factor by grouping.

17. Use the ac test to determine if the following trinomial can be factored. Find the values of m and n for the trinomial if it can be factored. x^2 + 2x - 15

18. Use the ac test to determine if the following trinomial can be factored. Find the values of m and n for the trinomial if it can be factored. x^2 -3x + 7

19. Rewrite the middle term as the sum of two terms and then factor completely. 12w^2 +19w +4

20. Rewrite the middle term as the sum of two terms and then factor completely. 4z^3 - 18z^2 - 10z

21. Factor the following polynomial completely. To begin, state which method should be applied as the first step. Then continue the exercise and factor the polynomial completely. 2p - 6q + pq - 3q^2

22. Factor the following polynomial completely. To begin, state which method should be applied as the first step. Then continue the exercise and factor the polynomial completely. m^4 - 9n^4

23. Factor completely: 9x^2 + 12xy + 4y^2 -25

24. Solve the following quadratic equation. 4x^2 = 13x + 12

25. Geometry. If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square?

#### Solution Summary

The solution is a detailed guide on the factoring the polynomial. It explains the various techniques, such as, grouping, extracting GCF, ac test for trinomial, difference of squares, and perfect squares, etc.