h(i) be the second derivative of p(i). Factor h(b).
2*b*(b - 2)*(2*b + 1)/3
Let c(i) = i**2 + 324*i + 26241. Let s(a) = -1. Let u(z) = c(z) - 3*s(z). Factor u(x).
(x + 162)**2
Let h = -19 - -32. Let b = -10 + h. Suppose s + 3*s**3 - s**4 + 27 - 27 - b*s**2 = 0. Calculate s.
0, 1
Suppose 3*g - 2*g + 2*f = -3, -5*g + 3 = 4*f. Suppose 0 = -g*x + 4*o + 1044, -696 = -2*x - 3*o - o. Factor 4*v**5 - 348 + x + 4*v**3 - 8*v**4.
4*v**3*(v - 1)**2
Let d(j) be the first derivative of -15/8*j + 3/4*j**2 + 15 + 1/8*j**3. Solve d(w) = 0.
-5, 1
Let x(h) be the second derivative of 4*h + 1/6*h**4 + 3*h**2 + 0 + 4/3*h**3. Factor x(z).
2*(z + 1)*(z + 3)
Let s be 46/(-4)*-4 + -2. Factor -52*c - 4 - s*c**2 - 5 - 2 + 3.
-4*(c + 1)*(11*c + 2)
Solve 40/3*s**3 + 0*s - 16/3*s**4 - 32/3*s**2 + 2/3*s**5 + 0 = 0 for s.
0, 2, 4
Let q(g) be the second derivative of g**7/210 - g**6/25 + 2*g**5/25 + 2*g + 67. Factor q(y).
y**3*(y - 4)*(y - 2)/5
Find m such that -8*m**2 + 12*m**2 - 4*m**4 + 0*m**4 = 0.
-1, 0, 1
Let k be (2 + -16)/(-1) - 16/(-12). Suppose g**3 + 52/3*g - 3/2*g**4 + 16/3 + k*g**2 = 0. Calculate g.
-2, -2/3, 4
Suppose -14 = -5*s + 6. Suppose -2*p**4 - 12*p**2 + 6*p + 8 + 6*p**4 - 2*p - s*p**3 = 0. Calculate p.
-1, 1, 2
Let u(h) be the first derivative of h**9/4536 - h**7/252 + h**5/45 - 8*h**3/3 + 18. Let z(c) be the third derivative of u(c). Determine j, given that z(j) = 0.
-2, -1, 0, 1, 2
Let r(y) be the third derivative of -y**5/20 - 2*y**4 - 6*y**2 + 7. Factor r(s).
-3*s*(s + 16)
Let h(g) be the first derivative of g**5/300 - g**2/2 - 2. Let f(y) be the second derivative of h(y). Determine m so that f(m) = 0.
0
Let m(y) = 6*y**2 + 4*y + 3. Let o be (-15)/20 + (-193)/4. Let j = 28 + o. Let u(l) = -l**2 - 1. Let n(x) = j*u(x) - 3*m(x). Factor n(d).
3*(d - 2)**2
Let w(a) be the second derivative of 2*a + 2*a**3 + 0*a**2 + 1/3*a**4 - 2/15*a**6 + 0 - 3/5*a**5. Solve w(r) = 0 for r.
-3, -1, 0, 1
Let m = 877 + -877. Factor m - 4/3*i**2 + 4/3*i**4 + 4/3*i - 4/3*i**3.
4*i*(i - 1)**2*(i + 1)/3
Suppose 26*x - 30*x = -40. Suppose -6*r = -x*r + 12. Let 6*u**2 + 3 - 3 + u**r - 3*u - 4*u**3 = 0. Calculate u.
0, 1
Let 4*y**4 + 0 + 2/7*y**2 - 30/7*y**3 + 0*y = 0. Calculate y.
0, 1/14, 1
Factor -33/5*i + 3/5*i**2 + 6.
3*(i - 10)*(i - 1)/5
Let s(g) be the second derivative of -g**6/45 - g**5/3 - 11*g**4/6 - 40*g**3/9 - 16*g**2/3 - 25*g. Factor s(t).
-2*(t + 1)**2*(t + 4)**2/3
Let x(a) be the third derivative of a**6/264 + 41*a**5/660 + 83*a**4/264 + 5*a**3/22 - 2*a**2 - 79*a. Factor x(t).
(t + 3)*(t + 5)*(5*t + 1)/11
Suppose -75/8*w**5 + 0*w**2 + 0*w - 3/2*w**3 + 0 + 15/2*w**4 = 0. What is w?
0, 2/5
Let f = -807 + 807. Find i such that -15*i**4 + f + 15*i**2 - 10/3*i - 25/3*i**3 + 35/3*i**5 = 0.
-1, 0, 2/7, 1
Let r(j) be the first derivative of -j**4/36 - j**3/9 + 6*j - 22. Let k(z) be the first derivative of r(z). Let k(l) = 0. Calculate l.
-2, 0
Let q(z) be the first derivative of 2*z**3 - z**2/2 - 19*z + 2. Let h = -5 - 2. Let a(x) = -4*x**2 + x + 13. Let s(o) = h*a(o) - 5*q(o). Factor s(i).
-2*(i - 1)*(i + 2)
Let a(j) be the third derivative of j**7/315 - j**6/30 + 13*j**5/90 - j**4/3 + 4*j**3/9 + 3*j**2 - 75. Factor a(n).
2*(n - 2)**2*(n - 1)**2/3
Let l(g) be the first derivative of 4*g**3/3 + 12*g**2 - 28*g + 22. What is a in l(a) = 0?
-7, 1
Let q(p) = -250*p**2 + 240*p + 35. Let g(f) = -21*f**2 + 20*f + 3. Let z(l) = 25*g(l) - 2*q(l). Factor z(h).
-5*(h - 1)*(5*h + 1)
Let b = -52/21 + 22/7. Let q = -25/21 - -13/7. Factor -q*f**2 + 4/3 - b*f.
-2*(f - 1)*(f + 2)/3
Let 3*h**3 - 37 + 574*h + 1 + 9*h**2 - 586*h = 0. Calculate h.
-3, -2, 2
Let y be (-2)/(-4) + 45/10. Factor 440*p**3 - 2*p**y - 444*p**3 - p + p + 6*p**4.
-2*p**3*(p - 2)*(p - 1)
Let u be ((-58)/10 - (-6 - -2))*-3. Suppose -114/5*m**4 - u*m**5 + 0 - 132/5*m**3 - 24/5*m**2 + 0*m = 0. What is m?
-2, -2/9, 0
Let s(n) be the second derivative of -n**4/24 + 16*n**3/3 + 65*n**2/4 + n + 27. Factor s(d).
-(d - 65)*(d + 1)/2
Let u(s) be the third derivative of -3*s**6/20 + 7*s**5/30 + 5*s**4/3 + 4*s**3/3 - 61*s**2 - s. Determine m so that u(m) = 0.
-1, -2/9, 2
Let -3/4 - 13/8*f**3 + 11/8*f**2 + 13/8*f - 5/8*f**4 = 0. What is f?
-3, -1, 2/5, 1
Let q be (50/5 + -8)/((-39)/(-18)). Suppose 0 - 2*k**2 - 14/13*k**4 - 4*k**3 + q*k = 0. Calculate k.
-3, -1, 0, 2/7
Let a(q) be the third derivative of q**10/604800 - q**8/80640 + 11*q**5/60 + 9*q**2. Let g(s) be the third derivative of a(s). Factor g(b).
b**2*(b - 1)*(b + 1)/4
Let c(w) be the first derivative of 4*w**3 + 0*w**2 - 3 - 1/450*w**6 + 0*w - 1/15*w**4 - 1/50*w**5. Let d(h) be the third derivative of c(h). Factor d(f).
-4*(f + 1)*(f + 2)/5
Let u(d) be the first derivative of d**2 + 0*d + 2*d**3 + 2/5*d**5 + 3/2*d**4 + 14. Solve u(k) = 0.
-1, 0
Let i = 4483 - 31365/7. Factor 2/7*h**3 + i + 24/7*h + 12/7*h**2.
2*(h + 2)**3/7
Let -6*w**2 + w + 12 - 24*w**3 + 20*w - 168*w**5 + 171*w**5 - 6*w**4 = 0. Calculate w.
-1, 1, 4
Suppose 1024 = 5*f + 999. Let y(h) be the third derivative of 2*h**2 + 5/12*h**4 - 4/45*h**6 + 0 - 2/9*h**3 + 0*h - 4/15*h**f. Factor y(l).
-2*(l + 2)*(4*l - 1)**2/3
Let c(a) = 12*a**3 - 10*a**2 - 36*a - 14. Let g(t) = 10*t**3 - 10*t**2 - 34*t - 14. Let l(b) = 4*c(b) - 5*g(b). Find m, given that l(m) = 0.
-1, 7
Suppose 22 + 2 = 6*w. Suppose w*j - 55 = -b - 24, 5*b - 5*j - 105 = 0. Let 0*t**3 + 21*t - b*t + 3*t**2 + t**3 - 2*t**3 = 0. Calculate t.
0, 1, 2
Suppose -2*y - 6 = -4*y. Suppose -y*u - m - m = 1, u + 17 = -4*m. Suppose 0*r - 3*r**4 - r**u + 3*r**2 + 0*r**4 + r = 0. What is r?
-1, -1/3, 0, 1
Let y(v) be the second derivative of 0 - 13/20*v**5 - 32*v**2 - 56/3*v**3 - 5*v**4 - 1/30*v**6 + 12*v. Factor y(k).
-(k + 1)*(k + 4)**3
Let u(x) be the second derivative of -1/3*x**4 - 6*x**2 - 8/3*x**3 + 0 + 30*x. Solve u(z) = 0.
-3, -1
Factor 59*j - 133*j - 107811*j**3 - 223*j + 3 + 9801*j**2.
-3*(33*j - 1)**3
Let b(u) be the first derivative of 5*u**2 + 2/5*u**5 + 0*u - 15 + 22/3*u**3 + 7/2*u**4. Factor b(l).
2*l*(l + 1)**2*(l + 5)
Solve 9/2*z**2 - 1/2*z**3 - 12*z + 10 = 0 for z.
2, 5
Let z(y) be the third derivative of -1/315*y**7 + 1/12*y**3 - 1/180*y**6 + 0*y + 23*y**2 - 7/72*y**4 + 19/360*y**5 + 0. What is r in z(r) = 0?
-3, 1/2, 1
Let f be (-20)/(-110) + (-489)/(-33). Let s be 0 - 6/f*30/(-8). Factor 21/4*h + 9/4*h**2 + s.
3*(h + 2)*(3*h + 1)/4
Let f(y) be the second derivative of 6*y**6/5 - 92*y**5/5 - 196*y**4/3 + 32*y**3 - 35*y - 6. Factor f(r).
4*r*(r - 12)*(r + 2)*(9*r - 2)
Factor 0*m + 0 + 2/19*m**2 - 2/19*m**3.
-2*m**2*(m - 1)/19
Let n(l) be the first derivative of -l**5/90 - 5*l**4/36 - 2*l**3/3 + 12*l**2 - 10. Let j(b) be the second derivative of n(b). Factor j(u).
-2*(u + 2)*(u + 3)/3
Factor 1/7*h**2 - 30/7 - 1/7*h.
(h - 6)*(h + 5)/7
Let g(j) = -j**3 - 1. Let p(k) = 26*k**3 - 17*k**3 + 6*k - 25 + 11*k**2 - 3*k**2. Let y(w) = 22*g(w) + 2*p(w). Suppose y(z) = 0. What is z?
-2, 3
Let s(u) be the first derivative of 2/21*u - 1/21*u**4 + 0*u**3 + 2/21*u**2 - 2/105*u**5 - 34. Factor s(l).
-2*(l - 1)*(l + 1)**3/21
Let c = 33 - 29. Suppose -z**2 - c + z + 16 - 8 - 2 = 0. What is z?
-1, 2
Let b(x) be the first derivative of 3/4*x**5 + 7/2*x**4 + 3/4*x**2 + 0*x + 6 + 35/12*x**3. Solve b(h) = 0 for h.
-3, -2/5, -1/3, 0
Suppose 4*x - 8 = 2*k, 5*k + 3*x - x - 16 = 0. Let o be 8/(-2 + 6) - k. Solve o*h**2 + h**2 + 2*h**2 - 3*h**4 + 6*h - 6*h**3 = 0.
-2, -1, 0, 1
Let t = -12370 + 12373. Find w such that 4*w**2 + 1/6*w**4 - 4/3*w**t + 8/3 - 16/3*w = 0.
2
Let n(r) be the first derivative of 2*r**5/5 + 10*r**4 + 154*r**3/3 - 242*r**2 - 987. Factor n(l).
2*l*(l - 2)*(l + 11)**2
Let v(d) = 3*d**3 - 17*d**2 + 12*d - 2. Let i(t) = 7*t**3 - 35*t**2 + 23*t - 5. Let p(j) = -4*i(j) + 10*v(j). Solve p(f) = 0.
0, 1, 14
Let f = -63 - -45. Let u be (48/36)/((-8)/f). Suppose 0 + q**u - 1/3*q + 2/3*q**2 = 0. What is q?
-1, 0, 1/3
Let f be (18/15)/(3/(-10)). Let z = -1 - f. Suppose -3*x**2 - 3*x**4 + 0*x**3 + 2*x**3 - 8*x**z + 0*x**4 = 0. What is x?
-1, 0
Let b(w) be the first derivative of -9/5*w**5 + 0*w**2 + 3*w**4 + 1 - w**3 + 0*w. Factor b(k).
-3*k**2*(k - 1)*(3*k - 1)
Let d be 3/1 - (11 + 516/(-54)). Factor d*m**2 + 2/3*m**4 + 4/9*m + 0 + 16/9*m**3.
2*m*(m + 1)**2*(3*m + 2)/9
Let g(o) = -2*o**5 - o**4 + 5*o**3 - 5*o**2 + 9*o + 6. Let b(y) = -y**3 + 7*y**4 - 1 + 4*y - 6