2. $81 - 25x^2$
3. $x^2 + 14x + 49$
4. $4x^2 - 44x + 121$
5. $64x^2 - 9y^2$
6. $100x^2 - 20x + 1$
7. $3x^2 - 3$
8. $-x^2 + 144$
9. $4x^2 - 16x + 16$
10. $-18x^2 + 60x - 50$

solve the equation.
11. $x^2 - 64 = 0$
12. $49 - 4x^2 = 0$
13. $x^2 = 8x - 16$
14. $36x^2 = -12x - 1$

15. you drop a penny while taking change out of your pocket. the function $y = 49 - 9t^2$ represents the height $y$ (in feet) of the penny $t$ seconds after falling from your pocket. after how many seconds...

Question

2. $81 - 25x^2$
3. $x^2 + 14x + 49$
4. $4x^2 - 44x + 121$
5. $64x^2 - 9y^2$
6. $100x^2 - 20x + 1$
7. $3x^2 - 3$
8. $-x^2 + 144$
9. $4x^2 - 16x + 16$
10. $-18x^2 + 60x - 50$

solve the equation.
11. $x^2 - 64 = 0$
12. $49 - 4x^2 = 0$
13. $x^2 = 8x - 16$
14. $36x^2 = -12x - 1$

15. you drop a penny while taking change out of your pocket. the function $y = 49 - 9t^2$ represents the height $y$ (in feet) of the penny $t$ seconds after falling from your pocket. after how many seconds...

Accepted Answer

{ "quality": "clear", "question_count": 14, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Factoring Polynomials", "Solving Quadratic Equations" ], "current_concepts": [ "Factoring Polynomials", "Solving Quadratic Equations" ] } ## Factor expressions 2 to 10 $$ \begin{aligned} \text{2. } & 81 - 25x^2 = (9 - 5x)(9 + 5x) \ \text{3. } & x^2 + 14x + 49 = (x + 7)^2 \ \text{4. } & 4x^2 - 44x + 121 = (2x - 11)^2 \ \text{5. } & 64x^2 - 9y^2 = (8x - 3y)(8x + 3y) \ \text{6. } & 100x^2 - 20x + 1 = (10x - 1)^2 \ \text{7. } & 3x^2 - 3 = 3(x^2 - 1) = 3(x - 1)(x + 1) \ \text{8. } & -x^2 + 144 = 144 - x^2 = (12 - x)(12 + x) \ \text{9. } & 4x^2 - 16x + 16 = 4(x^2 - 4x + 4) = 4(x - 2)^2 \ \text{10. } & -18x^2 + 60x - 50 = -2(9x^2 - 30x + 25) = -2(3x - 5)^2 \end{aligned} $$ ## Solve equations 11 to 14 $$ \begin{aligned} \text{11. } & x^2 - 64 = 0 \implies x^2 = 64 \implies x = \pm 8 \ \text{12. } & 49 - 4x^2 = 0 \implies 4x^2 = 49 \implies x^2 = \frac{49}{4} \implies x = \pm \frac{7}{2} \ \text{13. } & x^2 = 8x - 16 \implies x^2 - 8x + 16 = 0 \implies (x - 4)^2 = 0 \implies x = 4 \ \text{14. } & 36x^2 = -12x - 1 \implies 36x^2 + 12x + 1 = 0 \implies (6x + 1)^2 = 0 \implies x = -\frac{1}{6} \end{aligned} $$ | No. | Answer | |---|---| | 2 | $(9 - 5x)(9 + 5x)$ | | 3 | $(x + 7)^2$ | | 4 | $(2x - 11)^2$ | | 5 | $(8x - 3y)(8x + 3y)$ | | 6 | $(10x - 1)^2$ | | 7 | $3(x - 1)(x + 1)$ | | 8 | $(12 - x)(12 + x)$ | | 9 | $4(x - 2)^2$ | | 10 | $-2(3x - 5)^2$ | | 11 | $x = \pm 8$ | | 12 | $x = \pm \frac{7}{2}$ | | 13 | $x = 4$ | | 14 | $x = -\frac{1}{6}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

No.	Answer
3	\((x + 7)^2\)
4	\((2x - 11)^2\)
5	\((8x - 3y)(8x + 3y)\)
6	\((10x - 1)^2\)
7	\(3(x - 1)(x + 1)\)
8	\((12 - x)(12 + x)\)
9	\(4(x - 2)^2\)
10	\(-2(3x - 5)^2\)
11	\(x = \pm 8\)
12	\(x = \pm \frac{7}{2}\)
13	\(x = 4\)
14	\(x = -\frac{1}{6}\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Factor expressions 2 to 10

Solve equations 11 to 14

Answer: