UST Middle School Algebra I Challenge
Week 9 — Polynomials & Factoring Basics
Focus: Adding/multiplying polynomials, GCF, simple trinomials
Weekly Format
Week 9
Part A — 15 Multiple Choice
Part B — 15 Fill in the Blank
Part C — 15 Word / Open-Response Problems
Part D — 5 Challenge Problems
Answer key and step-by-step explanations follow the questions.
Part A — Multiple Choice
Questions 1–5
1. Expand (x+3)(x+2). A) x²+5x+6 B) x²+6 C) 2x²+3x+2 D) x²+3x+2
2. Expand (x+4)(x+2). A) x²+6x+8 B) x²+8 C) 2x²+4x+2 D) x²+4x+2
3. Expand (x+5)(x+2). A) x²+7x+10 B) x²+10 C) 2x²+5x+2 D) x²+5x+2
4. Expand (x+6)(x+2). A) x²+8x+12 B) x²+12 C) 2x²+6x+2 D) x²+6x+2
5. Expand (x+7)(x+2). A) x²+9x+14 B) x²+14 C) 2x²+7x+2 D) x²+7x+2
Part A — Multiple Choice
Questions 6–10
6. Expand (x+8)(x+2). A) x²+10x+16 B) x²+16 C) 2x²+8x+2 D) x²+8x+2
7. Expand (x+9)(x+2). A) x²+11x+18 B) x²+18 C) 2x²+9x+2 D) x²+9x+2
8. Expand (x+10)(x+2). A) x²+12x+20 B) x²+20 C) 2x²+10x+2 D) x²+10x+2
9. Expand (x+11)(x+2). A) x²+13x+22 B) x²+22 C) 2x²+11x+2 D) x²+11x+2
10. Expand (x+12)(x+2). A) x²+14x+24 B) x²+24 C) 2x²+12x+2 D) x²+12x+2
Part A — Multiple Choice
Questions 11–15
11. Expand (x+13)(x+2). A) x²+15x+26 B) x²+26 C) 2x²+13x+2 D) x²+13x+2
12. Expand (x+14)(x+2). A) x²+16x+28 B) x²+28 C) 2x²+14x+2 D) x²+14x+2
13. Expand (x+15)(x+2). A) x²+17x+30 B) x²+30 C) 2x²+15x+2 D) x²+15x+2
14. Expand (x+16)(x+2). A) x²+18x+32 B) x²+32 C) 2x²+16x+2 D) x²+16x+2
15. Expand (x+17)(x+2). A) x²+19x+34 B) x²+34 C) 2x²+17x+2 D) x²+17x+2
Part B — Fill in the Blank
Questions 16–20
16. Factor x²+5x+6: ___.
17. Factor x²+6x+9: ___.
18. Factor x²+7x+12: ___.
19. Factor x²+8x+15: ___.
20. Factor x²+9x+18: ___.
Part B — Fill in the Blank
Questions 21–25
21. Factor x²+10x+21: ___.
22. Factor x²+11x+24: ___.
23. Factor x²+12x+27: ___.
24. Factor x²+13x+30: ___.
25. Factor x²+14x+33: ___.
Part B — Fill in the Blank
Questions 26–30
26. Factor x²+15x+36: ___.
27. Factor x²+16x+39: ___.
28. Factor x²+17x+42: ___.
29. Factor x²+18x+45: ___.
30. Factor x²+19x+48: ___.
Part C — Word / Open Response
Questions 31–35
31. A rectangle has side lengths x+2 and x+3. Write its area as a polynomial.
32. A rectangle has side lengths x+3 and x+3. Write its area as a polynomial.
33. A rectangle has side lengths x+4 and x+3. Write its area as a polynomial.
34. A rectangle has side lengths x+5 and x+3. Write its area as a polynomial.
35. A rectangle has side lengths x+6 and x+3. Write its area as a polynomial.
Part C — Word / Open Response
Questions 36–40
36. A rectangle has side lengths x+7 and x+3. Write its area as a polynomial.
37. A rectangle has side lengths x+8 and x+3. Write its area as a polynomial.
38. A rectangle has side lengths x+9 and x+3. Write its area as a polynomial.
39. A rectangle has side lengths x+10 and x+3. Write its area as a polynomial.
40. A rectangle has side lengths x+11 and x+3. Write its area as a polynomial.
Part C — Word / Open Response
Questions 41–45
41. A rectangle has side lengths x+12 and x+3. Write its area as a polynomial.
42. A rectangle has side lengths x+13 and x+3. Write its area as a polynomial.
43. A rectangle has side lengths x+14 and x+3. Write its area as a polynomial.
44. A rectangle has side lengths x+15 and x+3. Write its area as a polynomial.
45. A rectangle has side lengths x+16 and x+3. Write its area as a polynomial.
Part D — Challenge
Questions 46–50
46. Challenge: Factor x²−6x+8.
47. Challenge: Factor x²−7x+12.
48. Challenge: Factor x²−8x+16.
49. Challenge: Factor x²−9x+20.
50. Challenge: Factor x²−10x+24.
Answer Key — Questions 1–5
Answer + How to Solve
1. Answer: A
How to solve: FOIL: x²+2x+3x+6=x²+5x+6.
2. Answer: A
How to solve: FOIL: x²+2x+4x+8=x²+6x+8.
3. Answer: A
How to solve: FOIL: x²+2x+5x+10=x²+7x+10.
4. Answer: A
How to solve: FOIL: x²+2x+6x+12=x²+8x+12.
5. Answer: A
How to solve: FOIL: x²+2x+7x+14=x²+9x+14.
Answer Key — Questions 6–10
Answer + How to Solve
6. Answer: A
How to solve: FOIL: x²+2x+8x+16=x²+10x+16.
7. Answer: A
How to solve: FOIL: x²+2x+9x+18=x²+11x+18.
8. Answer: A
How to solve: FOIL: x²+2x+10x+20=x²+12x+20.
9. Answer: A
How to solve: FOIL: x²+2x+11x+22=x²+13x+22.
10. Answer: A
How to solve: FOIL: x²+2x+12x+24=x²+14x+24.
Answer Key — Questions 11–15
Answer + How to Solve
11. Answer: A
How to solve: FOIL: x²+2x+13x+26=x²+15x+26.
12. Answer: A
How to solve: FOIL: x²+2x+14x+28=x²+16x+28.
13. Answer: A
How to solve: FOIL: x²+2x+15x+30=x²+17x+30.
14. Answer: A
How to solve: FOIL: x²+2x+16x+32=x²+18x+32.
15. Answer: A
How to solve: FOIL: x²+2x+17x+34=x²+19x+34.
Answer Key — Questions 16–20
Answer + How to Solve
16. Answer: (x+3)(x+2)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
17. Answer: (x+3)(x+3)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
18. Answer: (x+3)(x+4)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
19. Answer: (x+3)(x+5)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
20. Answer: (x+3)(x+6)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
Answer Key — Questions 21–25
Answer + How to Solve
21. Answer: (x+3)(x+7)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
22. Answer: (x+3)(x+8)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
23. Answer: (x+3)(x+9)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
24. Answer: (x+3)(x+10)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
25. Answer: (x+3)(x+11)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
Answer Key — Questions 26–30
Answer + How to Solve
26. Answer: (x+3)(x+12)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
27. Answer: (x+3)(x+13)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
28. Answer: (x+3)(x+14)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
29. Answer: (x+3)(x+15)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
30. Answer: (x+3)(x+16)
How to solve: Find two numbers with sum n+3 and product 3n: 3 and n.
Answer Key — Questions 31–35
Answer + How to Solve
31. Answer: x²+5x+6
How to solve: Multiply the binomials using distribution/FOIL.
32. Answer: x²+6x+9
How to solve: Multiply the binomials using distribution/FOIL.
33. Answer: x²+7x+12
How to solve: Multiply the binomials using distribution/FOIL.
34. Answer: x²+8x+15
How to solve: Multiply the binomials using distribution/FOIL.
35. Answer: x²+9x+18
How to solve: Multiply the binomials using distribution/FOIL.
Answer Key — Questions 36–40
Answer + How to Solve
36. Answer: x²+10x+21
How to solve: Multiply the binomials using distribution/FOIL.
37. Answer: x²+11x+24
How to solve: Multiply the binomials using distribution/FOIL.
38. Answer: x²+12x+27
How to solve: Multiply the binomials using distribution/FOIL.
39. Answer: x²+13x+30
How to solve: Multiply the binomials using distribution/FOIL.
40. Answer: x²+14x+33
How to solve: Multiply the binomials using distribution/FOIL.
Answer Key — Questions 41–45
Answer + How to Solve
41. Answer: x²+15x+36
How to solve: Multiply the binomials using distribution/FOIL.
42. Answer: x²+16x+39
How to solve: Multiply the binomials using distribution/FOIL.
43. Answer: x²+17x+42
How to solve: Multiply the binomials using distribution/FOIL.
44. Answer: x²+18x+45
How to solve: Multiply the binomials using distribution/FOIL.
45. Answer: x²+19x+48
How to solve: Multiply the binomials using distribution/FOIL.
Answer Key — Questions 46–50
Answer + How to Solve
46. Answer: (x−4)(x−2)
How to solve: Find two negative numbers with sum −(n+4) and product 4n.
47. Answer: (x−4)(x−3)
How to solve: Find two negative numbers with sum −(n+4) and product 4n.
48. Answer: (x−4)(x−4)
How to solve: Find two negative numbers with sum −(n+4) and product 4n.
49. Answer: (x−4)(x−5)
How to solve: Find two negative numbers with sum −(n+4) and product 4n.
50. Answer: (x−4)(x−6)
How to solve: Find two negative numbers with sum −(n+4) and product 4n.