## MATH 114N Week 3 Test 1 Chapter 13 | Solutions

. **Question: **Factor the trinomial completely.

– 45h^{3} + 150h^{2}y – 125hy^{2}

**2. Question: **Factor by grouping.

3u^{3} + 8u – 3

**3. Question: **Factor completely.

64a^{2} – 25t^{2}

**4. Question: **Factor completely.

v^{2} + 64

**5. Question: **Factor completely.

9x^{2} – 12xy + 4y^{2}

**6. Question: **Solve.

25t^{2} – 16 = 0

**7. Question: **Factor the trinomial completely.

14m^{2} – 43m + 20

**8. Question: **Factor the following polynomial by grouping.

3xy + 12x + 2y + 8

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## STATUS

3xy + 12x + 2y + 8 = (y + 4)(3x + 2)

**9. Question: **Write in factored form by factoring out the greatest common factor (or a negative common factor if the coefficient of the term of greatest degree is negative).

– 8x^{6} – 4x^{5}

**10. Question: **Factor the trinomial.

r^{2} + 2r – 63

**11. Question: **Find all solutions by factoring.

b^{2} + 13b + 42 = 0

**12. Question: **If a trinomial has a negative coefficient for the second-degree term, it may be easier to factor by first factoring out -1. Use this method to factor the following trinomial.

– v^{2} – 3v + 88

**13. Question: **Complete the factoring.

2x^{3} + 8x^{2} + 6x

**14. Question: **Factor the trinomial.

t^{2} – 18t + 80

**15. Question: **The length of the top of the table is 6m greater than the width. The area is 91m^{2}. Find the dimensions of the table.

**16. Question: **Factor.

b^{2} + 10b + 25

**17. Question: **Solve the equation and check your solutions.

z^{2} + 4z = –3

**18. Question: **A ladder is leaning against a building. The distance from the bottom of the ladder is 18 ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 1 ft less than the length of the ladder.

**19. Question: **Factor completely.

b^{2} – 64

**20. Question: **Factor. Note that the middle term has already been split.

c^{2} – 3c – c + 3

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c^{2} – 3c – c + 3 = (c – 3)(c – 1)

**21. Question: **Factor the trinomial completely.

4b^{2} + 15b + 9

**22. Question: **Factor the trinomial completely.

3n^{2} – 6n + 3

**23. Question: **Solve the equation.

(7x – 6)(4x + 4) = 0

**24. Question: **Factor the trinomial completely.

– 45h^{3} + 150h^{2}y – 125y^{2}

**25. Question: **Factor the following polynomial completely.

r^{4} – 1

**26. Question: **Factor the trinomial.

a^{2} – 2ax – 63x^{2}