Math help?
= (3x³ + 4x² - 5x - 2)/(x + 2) First term: 3x³/x = 3x² 3x².(x + 2) = 3x³ + 6x² Rest: = (3x³ + 4x² - 5x - 2) - (3x³ + 6x²) = 3x³ + 4x² - 5x - 2 - 3x³ - 6x² = - 2x² - 5x - 2 Second term: - 2x²/x = - 2x - 2x.(x + 2) = - 2x² - 4x Rest: = (- 2x² - 5x - 2) - (- 2x² - 4x) = - 2x² - 5x - 2 + 2x² + 4x = - x - 2 Third term: - x/x = - 1 - 1.(x + 2) = - x - 2 Rest: = (- x - 2) - (- x - 2) = - x - 2 + x + 2 = 0 ← this is the remainder 3x³ + 4x² - 5x - 2 = [(x + 2).(3x² - 2x - 1)] + 0 3x³ + 4x² - 5x - 2 = (x + 2).(3x² - 2x - 1) (3x³ + 4x² - 5x - 2)/(x + 2) = 3x² - 2x - 1 = (2x³ + 4x² + 3x + 4)/(x + 1) First term: 2x³/x = 2x² 2x².(x + 1) = 2x³ + 2x² Rest: = (2x³ + 4x² + 3x + 4) - (2x³ + 2x²) = 2x³ + 4x² + 3x + 4 - 2x³ - 2x² = 2x² + 3x + 4 Second term: 2x²/x = 2x 2x.(x + 1) = 2x² + 2x Rest: = (2x² + 3x + 4) - (2x² + 2x) = 2x² + 3x + 4 - 2x² - 2x = x + 4 Third term: x/x = 1 (x + 1) = x + 1 Rest: = (x + 4) - (x + 1) = x + 4 - x - 1 = 3 ← this is the remainder 2x³ + 4x² + 3x + 4 = [(x + 1).(2x² + 2x + 1)] + 3 (2x³ + 4x² + 3x + 4)/(x + 1) = 2x² + 2x + 1 + [3/(x + 1)] x + 3 to completely factor y = 4x3 + 5x2 – 23x – 6. y = 4x³ + 5x² - 23x - 6 y = (x + 3).(4x² + ax + b) → you expand y = 4x³ + ax² + bx + 12x² + 3ax + 3b → you group y = 4x³ + x².(a + 12) + x.(b + 3a) + 3b → you compare with: 4x³ + 5x² - 23x - 6 3b = - 6 → b = - 2 b + 3a = - 23 → 3a = - 23 - b → 3a = - 21 → a = - 7 a + 12 = 5 → a = - 7 → of course, see above y = (x + 3).(4x² + ax + b) y = (x + 3).(4x² - 7x - 2)
Algebra 2 help?
3. Which is equal to (4x^2 + 3x - 1) + (-3x^2- 5x - 8)? (Points : 4) x2- 2x + 9 x2 + 2x + 9 x2- 2x - 9 x4 - 2x^2- 9 Question 4.4. Which is equal to (2x^2- 5x + 4) (4x2 + 3x - 2)? (Points : 4) - 2x^2 8x + 6 6x^2 - 2x + 2 2x^2 - 2x + 2 2x^4 - 8x2 + 6 Question 5.5. Which is equal to (4x + 1)(3x - 2)? (Points : 4) 12x^2- 5x 2 7x^2 - 5x + 2 12x^2 + 5x- 2 12x^2 - 2 7. Which represents 4x^3 + 18x^2 + 2x in factored form? (Points : 4) 2x(2x^3 + 9x2 + x) 2x(2x^2 + 18x2 + x) 2x(2x^2 + 9x + 1) 2x(4x^2 + 18x + 1) Question 8.8. Which represents 25x^2 - 81 in factored form? (Points : 4) (5x + 9)(5x + 9) (5x - 9)(5x- 9) (5x + 9)(5x - 9) (5x + 3)(5x- 3) Question 9.9. Which represents x^2 + 8^x + 16 in factored form? (Points : 4) (x + 4)^2 (x + 4)(x - 4) (x - 4)^2 (x- 2)(x - 8) Question 10.10. Which represents x^2 + 7^x 60 in factored form? (Points : 4) (x - 5)(x - 12) (x - 6)(x + 10) (x + 5)(x - 12) (x 5)(x + 12) 12. Which is the equation of the power function p(x) = ax^3 where p(2) = 48? (Points : 4) p(x) = 24x^3 p(x) = 6x^3 p(x) = 6x^3 p(x) = 8x^3
Can anyone help me with factorization of [math]\lim_{x \rightarrow 1} \frac{x^3 + 3x^2 -6x + 2}{ x^3 + 3x^2 - 3x - 1}[/math]to solve the limit?
Since Lakshya Jain has already answered this question I won't do it again.Just a tip. When you want to find the limit of the Quotient of two polynomials when x->a Divide both polynomials by (x-a). This approach usually works.See: Polynomial Long Division
PLEASE HELP ME WITH MY MATH! I CANT FIGURE THIS STUFF OUT TO SAVE MY LIFE!?
1. Cubic trinomial (count the parts, check the equation's highest exponential degree) 2. 9x^3 + 6x^3 = 15x^3 12x^2 + 5x^2 = 17x^2 15x^3 + 17x^2 + 2x + 3 3. I hate it when you remove the minus signs and the ^s. (4x^2 + 3x + 1) + (3x^2 - 5x - 8) = 7x^2 - 2x - 7 4. it's (2x^2 + 5x + 4) - (4x2 - 3x + 2) -2x^2 + 8x + 2 5. (4x+1)(3x-2) = 12x^2 - 5x - 2 6. this question is not clear 7. 8x^3 - 12x^2 - 4x = 4x(2x^2 - 3x - 1) 8. 9x^2 = 4; 3x = +/- 2; 9x^2 - 4 = (3x + 2)(3x - 2) 9. find the number that gives a sum of 8 and a product of 16 x^2 + 8x + 16 = (x + 4)^2 10. find a and b such that a + b = -5 and a*b = -60 x^2 - 7x - 60 = (x + 5)(x - 12) 11. where's the graph? 12. p(2) = 48 = a(2)^3 = 8a; a = 48/8 = 6; p(x) = 6x^3
ALGEBRA 2 HELP? 10 POINTS! PLEASE HURRY!?
1. Which describes the polynomial 3x3 2x + 1? cubic trinomial Question 2.2. Use the polynomial to answer the question. 17x^3 - 15x^2 + 2x + 3 Question 3.3. Which is equal to (4x2 + 3x - 1) + (-3x^2 - 5x - 8)? x^2 - 2x - 9 Question 4.4. Which is equal to (2x^2 + 5x + 4) - (4x^2 - 3x + 2)? -2x^2 + 8x + 2 Question 5.5. Which is equal to (4x - 1)(3x + 2)? 12x^2 + 5x - 2 ****Question 6.6.***** Not sure on this one, need more information about the rectangle! Which represents the area of the rectangle? 2x^2 - 10 2x^2 + x - 10 2x^2 - 9x - 10 2x^2 - x - 10 Question 7.7. Which represents 6x^3 + 12x^2 - 9x in factored form? 3x(2x^2 + 4x - 3) Question 8.8. Which represents 4x^2 - 9 in factored form? (2x + 3)(2x - 3) Question 9.9. Which represents x2 + 8x + 16 in factored form? (x + 4)^2 Question 10.10. Which represents x^2 + 7x - 60 in factored form? (x - 5)(x + 12) Question 12.12. Which is the equation of the power function p(x) = ax^3 where p(2) = -64? p(x) = -8x^3
Algebra 2 help? Multiple choice :) Please and thank you!?
1. Which expression is not a polynomial? Option A: 1/3x Option B: x - 5 Option C: 4x^-1 + 5x > - 2 Option D: x^3 + 4x 3 2. Use the polynomial to answer the question. 3x3 + 4x2 7 Which describes the polynomial? quadratic trinomial cubic binomial quartic trinomial cubic trinomial 3. Use the polynomial to answer the question. 14x2 8 + 5x 6x2 + 2x Which expresses the polynomial in standard form? 8x^2 + 7x-8 20x^2 + 7x - 8 15x^2 - 8 8x^2 + 3x - 8 4. Simplify. (5x 2 + 3x2) + (4x + 3) 12x^4 + 1 3x^2 + 9x + 1 3x^2 + 9x - 1 3x^2 + x + 5 5. Simplify. (4x2 3x + 2) (2x2 + 5x 7) 2x^2 + 2x - 5 6x^2 + 2x - 5 2x^2 - 8x + 9 2x^2 - 2x - 5
I need lots of math help please sorry just got behind!!!!!!?
Question 1. 1. Add the following polynomials: (4x2 + 2x – 3) + (x2 – x + 9) (Points : 1) 5x2+x+6 4x2+x+6 5x2+x+5 4x2+x+5 Question 2. 2. Add the following polynomials: (x2 – x + 7) + (x2 + 3x + 1) (Points : 1) 2x2+2x-8 2x2+2x+8 2x2-2x+8 -2x2+2x+8 Question 3. 3. Add the following polynomials: (–3x2 + 3x + 3) + (–2x2 – 10x + 2) (Points : 1) -5x2-7x+5 5x2-7x+5 -5x2+7x+5 5x2-7x-5 Question 4. 4. Add the following polynomials: (7x2 + x + 13) + (2x2 – 5x + 10) (Points : 1) -9x2-4x+23 9x2+4x+23 9x2-4x-23 9x2-4x+23 Question 5. 5. Add the following polynomials: (–4x2 + 12x – 4) + (3x2 – 2x + 6) (Points : 1) x2-10x-2 -x2+10x+2 x2-10x+2 x2+10x-2 Question 6. 6. Add the following polynomials: (6x2 – 6x – 6) + (6x2 – 6x + 9) (Points : 1) 12x2-12x+3 12x2+12x-3 -12x2-12x+3 12x2+12x-3 Question 7. 7. Add the following polynomials: (x2 – 4x – 3) + (x2 – 3x – 7) (Points : 1) -2x2-7x-10 2x2+7x-10 2x2-7x-10 2x2-7x+10 Question 8. 8. Add the following polynomials: (x2 + 2x + 10) + (–4x2 – 2x + 4) (Points : 1) 3x2-14 -3x2+14 -3x2-14 3x2+14 Question 9. 9. Add the following polynomials: (3x2 – 2x – 1) + (2x2 – 9x + 1) (Points : 1) 5x2+11x -5x2+11x 5x2-11x -5x2-11x Question 10. 10. Add the following polynomials: (4x2 + x – 2) + (x2 – 3x + 1) (Points : 1) 5x2-2x-1 -5x2-2x-1 5x2+2x-1 5x2+2x+1 Question 11. 11. Subtract the following polynomials: (4x2 + 2x – 3) – (x2 – x + 9) (Points : 1) -3x2+3x-12 3x2-3x-12 3x2+3x-12 -3x2-3x-12 Question 12. 12. Subtract the following polynomials: (2x2 – x + 7) – (x2 + 3x + 1) (Points : 1) -x2-4x+6 x2+4x+6 x2-4x-6 x2-4x+6
Can someone please check if these are correct, PLEASE?
HELLOOOOO!!! I'm sure you tried hard, I did too. 1. You're having problems with the signs, the values of x² are both positive so the sum has to be positive, and sum of the positive 1 with the negative 1 gives you 0. The answer is 7x² + 9x 2. Simmilar mistake, the values of x² are both positive and 3 - 7 = -4. Then the answer 10x² + 7x - 4 3. It's almost correct, the minus symbol is at your right side, so the right elements are the ones which become negative. The answer: x² + 8x - 6 4. Same mistake, let me show you the procedure I hope it helps a bit: (12x² + 3x + 7) - (7x² + x + 9) 12x² + 3x + 7 - (7x² + x + 9) <-- as they are positive you can just take off the parenthesis 12x² + 3x + 7 - 7x² - x - 9 <-- as they had negative symbol they change their signs. 12x² - 7x² + 3x - x - 9 + 7 <-- group them 5x² + 2x - 2 <-- The correct answer! 5. You are multiplying!! Then you have to multiply first the numeric values (4)(1) = 4. Then similar variables (x³)(x⁴) = (x³⁺⁴) = x⁷. So the result is (4x³)(x⁴) = x⁷ 6. You are moltiplyin too. In this case you have to multiply each term of the left side with each of the right side: (3x + 1)(x - 2) (3x)(x) + (3x)(-2) + (1)(x) + (1)(-2) (3x²) + (-6x) + (x) + (-2) 3x² - 6x + x - 2 <-- Reducing 3x² - 5x - 2 7. Following the similar procedure in the exercise 6 you get the answer: (5x + 1)(2x - 2) = 10x² - 8x - 2 8. GOOD! y = 4x + 5 9. Almost! y = 4x - 11 10. Noup! =( The answer: 4x + 3 > 6x - 1 3 + 1 > 6x - 4x 4 > 2x 4/2 > x x < 2 11. Signs again (4x² + 2x + 1)(x - 5) = 4x³ + 2x² + x - 20x² - 10x - 5 = 4x³ - 18x² - 9x -5 12. GOOD!!! The answer: 7x³ - 27x² - x - 12 13. You are having the same mistakes as the past multiplications (6 and 7), you need to multiply every term of the left with every term in the right. Just like you did in 11 and 12 (4x + 3)² = (4x + 3) (4x + 3) = 16x + 24x + 9 Ufff! I got tired. Hope it helps. Good Night!
Lim as x approaches inifinity of (5x^2 + 3x) /2x^2. How do we find the limit of this?
Begin by noting that the limit, in its current form, is indeterminate. That is, if you were to 'sub in' infinity, you would have infinity/infinity, which is indeterminate.The 2 most common ways to deal with limits in indeterminate forms are L'Hopital's rule or factorisation/polynomial long division. In 99.9% of cases, the former method is by far the easier method.I will therefore use L'Hopital's rule to solve this problem.L'Hopital's rule tell us that if the limit of a quotient assumes the indeterminate form 0/0, or infinity/infinity, then we can differentiate both the numerator and the denominator until the limit takes on a determinate form.I begin by setting [math]f(x)=\frac{g(x)}{h(x)}[/math], where [math]g(x)=5x^{2} + 3x[/math], and [math]h(x)=2x^{2}[/math].As stated above, the limit is indeterminate:[math]L = \lim_{x \to \infty} f(x) = \frac{g(\infty)}{h(\infty)} = \frac{\infty}{\infty}[/math]I then take successive derivatives of both [math]g(x)[/math] and [math]h(x)[/math] until the limit assumes a determinate form:[math]L = \frac{g'(\infty)}{h'(\infty)} = \frac{\infty}{\infty}[/math][math]L = \frac{g''(\infty)}{h''(\infty)} = \frac{10}{4} = \frac{5}{2}[/math].Therefore the limit is [math]\frac{5}{2}[/math]