Question

topic: creating binomial quadratics. multiply. (use the distributive property, write in standard form.) 1. x(4x - 7) 2. 5x(3x + 10) 3. 3x(4x - 2) 4. the answers to problems 1, 2, & 3 are quadratics that can be represented in standard form ax² + bx + c. which coefficient, a, b, or c equals 0 for all of the exercises above? factor the following. (write the expressions as the product of two linear factors.) 5. x² + 4x 6. 7x² - 21x 7. 12x² + 60x 8. 8x² + 20x multiply 9. (x + 9)(x - 9) 10. (x + 2)(x - 2) 11. (6x + 5)(6x - 5) 12. (7x + 1)(7x - 1) 13. the answers to problems 9, 10, 11, &12 are quadratics that can be represented in standard form ax² + bx + c. which coefficient, a, b, or c equals 0 for all of the exercises above? set topic: factoring trinomials. factor the following quadratic expressions into two binomials. 14. x² + 14x + 45 15. x² + 18x + 45 16. x² + 46x + 45 17. x² + 11x + 24 18. x² + 10x + 24 19. x² + 14x + 24 20. x² + 12x + 36 21. x² + 13x + 36 22. x² + 20x + 36 23. x² - 15x - 100 24. x² + 20x + 100 25. x² + 29x + 100 mathematics vision project licensed under the creative commons attribution cc by 4.0 mathematicsvisionproject.org

Explanation:

Step1: Expand 1 - 3

1. \(x(4x - 7)=4x^{2}-7x\)
2. \(5x(3x + 10)=15x^{2}+50x\)
3. \(3x(4x - 2)=12x^{2}-6x\)

Step2: Analyze coefficients for 4

In \(ax^{2}+bx + c\), for the results of 1 - 3, \(c = 0\)

Step3: Factor 5 - 8

1. \(x^{2}+4x=x(x + 4)\)
2. \(7x^{2}-21x=7x(x - 3)\)
3. \(12x^{2}+60x=12x(x + 5)\)
4. \(8x^{2}+20x=4x(2x + 5)\)

Step4: Expand 9 - 12

1. \((x + 9)(x - 9)=x^{2}-81\)
2. \((x + 2)(x - 2)=x^{2}-4\)
3. \((6x + 5)(6x - 5)=36x^{2}-25\)
4. \((7x + 1)(7x - 1)=49x^{2}-1\)

Step5: Analyze coefficients for 13

In \(ax^{2}+bx + c\), for the results of 9 - 12, \(b = 0\)

Step6: Factor 14 - 25

1. \(x^{2}+14x + 45=(x + 5)(x+9)\)
2. \(x^{2}+18x + 45=(x + 3)(x + 15)\)
3. \(x^{2}+46x + 45=(x + 1)(x + 45)\)
4. \(x^{2}+11x + 24=(x + 3)(x + 8)\)
5. \(x^{2}+10x + 24=(x + 4)(x + 6)\)
6. \(x^{2}+14x + 24=(x + 2)(x + 12)\)
7. \(x^{2}+12x + 36=(x + 6)^{2}\)
8. \(x^{2}+13x + 36=(x + 4)(x + 9)\)
9. \(x^{2}+20x + 36=(x + 2)(x + 18)\)
10. \(x^{2}-15x - 100=(x - 20)(x+5)\)
11. \(x^{2}+20x + 100=(x + 10)^{2}\)
12. \(x^{2}+29x + 100=(x + 4)(x + 25)\)

Answer:

1. \(4x^{2}-7x\)
2. \(15x^{2}+50x\)
3. \(12x^{2}-6x\)
4. \(c = 0\)
5. \(x(x + 4)\)
6. \(7x(x - 3)\)
7. \(12x(x + 5)\)
8. \(4x(2x + 5)\)
9. \(x^{2}-81\)
10. \(x^{2}-4\)
11. \(36x^{2}-25\)
12. \(49x^{2}-1\)
13. \(b = 0\)
14. \((x + 5)(x+9)\)
15. \((x + 3)(x + 15)\)
16. \((x + 1)(x + 45)\)
17. \((x + 3)(x + 8)\)
18. \((x + 4)(x + 6)\)
19. \((x + 2)(x + 12)\)
20. \((x + 6)^{2}\)
21. \((x + 4)(x + 9)\)
22. \((x + 2)(x + 18)\)
23. \((x - 20)(x+5)\)
24. \((x + 10)^{2}\)
25. \((x + 4)(x + 25)\)