 second derivative of -2/15*v**3 + 1/60*v**4 - u*v + 0 + 3/10*v**2. Let c(j) = 0. What is j?
1, 3
Suppose 304 + 736 - 280 + 5*j**2 - 765*j = 0. Calculate j.
1, 152
Let n = -13 + 20. Factor 12 - 2*d - 13*d - 7*d**3 + 5*d**3 - n*d + 12*d**2.
-2*(d - 3)*(d - 2)*(d - 1)
Let t = 67 - 68. Let n be -1 + t + 0 + 5. Factor -2/3*f**n + 10/3*f**2 + 8/3 - 16/3*f.
-2*(f - 2)**2*(f - 1)/3
Let s = 269/235 + 59/47. Let s + 45*p**5 - 141/5*p**2 + 0*p + 69*p**4 - 9/5*p**3 = 0. Calculate p.
-1, -1/3, 2/5
Factor 80/9*c**3 - 2/9*c**4 - 26/3*c**2 + 0 + 0*c.
-2*c**2*(c - 39)*(c - 1)/9
Let x(g) = -g**2 + g - 1. Let w(q) = -q**3 - 10*q**2 + 7*q - 4. Let m(a) = -w(a) + 5*x(a). Let o be m(-5). Factor 3/2 + 27/2*u**2 - 6*u**3 - o*u.
-3*(u - 1)**2*(4*u - 1)/2
Let a(w) be the third derivative of 2*w**3 + w**2 + 0 - 1/2*w**4 + 0*w + 1/20*w**5. Determine y, given that a(y) = 0.
2
Let -4*s**4 + 83 - 4*s**3 - s**2 + 13*s**3 - 92 + 2*s**4 - 21*s = 0. Calculate s.
-1, -1/2, 3
Let k(m) be the third derivative of m**7/560 + m**6/960 - 7*m**5/240 - m**4/48 + m**3/6 - 48*m**2 + 2*m. What is t in k(t) = 0?
-2, -1, 2/3, 2
Let y(r) be the first derivative of -2*r**7/1155 - 7*r**6/660 - r**5/110 - 16*r**2 + 26. Let w(z) be the second derivative of y(z). Factor w(f).
-2*f**2*(f + 3)*(2*f + 1)/11
Let b(d) = -5*d**2 - 5*d + 10. Let z(p) = 2*p**2 + 7. Let n(f) = -3*f**2 - 10. Let r(o) = 5*n(o) + 7*z(o). Let x(j) = -b(j) - 10*r(j). Factor x(c).
5*c*(3*c + 1)
Determine i, given that 5/7*i**4 + 32/7 - 2/7*i**3 - 4*i**2 - 8/7*i + 1/7*i**5 = 0.
-4, -2, 1, 2
Let n(f) be the first derivative of -6*f - 10 + 1/7*f**2 + 1/42*f**4 - 2/21*f**3. Let v(h) be the first derivative of n(h). Factor v(l).
2*(l - 1)**2/7
Suppose 12 = -2*k + 6*k. Let t(v) = -v**4. Let z(g) = 10*g - 13*g**3 - 15*g + 4*g - 3*g**2 + 10*g**3. Let h(o) = k*z(o) + 3*t(o). Factor h(u).
-3*u*(u + 1)**3
Factor 122 + 126 + 3*x**2 + 67*x**2 - 98 + 5*x**3 + 215*x.
5*(x + 1)*(x + 3)*(x + 10)
What is j in 1/4*j**3 - 41/4*j**2 + 0 + 0*j = 0?
0, 41
Let q(s) = -7*s**2 - 228*s + 6498. Let o(r) = -3*r**2. Let d(t) = -6*o(t) + 2*q(t). What is m in d(m) = 0?
57
Let c(m) be the second derivative of -7/12*m**4 + 0*m**2 + 2/5*m**5 + 1/6*m**3 + 8/15*m**6 + 0 + 4*m. Determine x so that c(x) = 0.
-1, 0, 1/4
Let a(s) be the third derivative of -247*s**5/40 + s**4/8 + 3*s**2 - 43*s. Find l, given that a(l) = 0.
0, 2/247
Let l = -697/940 - -56/47. Let d(y) be the second derivative of -4*y + 0 + y**4 + 0*y**3 + 0*y**2 - l*y**5 - 1/10*y**6. Solve d(u) = 0 for u.
-4, 0, 1
Let k be 9/2 - (-36)/24. Let x(o) = -o**4 + 2*o**3 + o**2 + o + 3. Let a(y) = 4*y**4 - 9*y**3 - 4*y**2 - 4*y - 13. Let c(t) = k*a(t) + 26*x(t). Factor c(b).
-2*b*(b - 1)*(b + 1)**2
Let a(v) be the second derivative of -23*v + 1/20*v**5 + 0*v**2 + 0*v**3 + 0*v**6 + 0*v**4 - 1/42*v**7 + 0. Suppose a(x) = 0. Calculate x.
-1, 0, 1
Suppose 0 = -84*t + 214 + 206. Factor 0*c**2 - 4/9*c**3 + 2/9*c**t + 0*c**4 + 2/9*c + 0.
2*c*(c - 1)**2*(c + 1)**2/9
Let o(g) be the first derivative of 21*g**6/8 - 93*g**5/10 - 309*g**4/16 + 12*g**3 + 39*g**2/2 - 12*g + 51. Find s, given that o(s) = 0.
-1, 2/7, 2/3, 4
Let v = 667/306 - 21/17. Let r = v - 4/9. Determine q so that 1/4*q + 3/4*q**2 - 1/4*q**4 - r - 1/4*q**3 = 0.
-2, -1, 1
Suppose 0 = 78*m - 69*m - 45. Let v(n) be the first derivative of -1/3*n**6 + 0*n**2 - 3/2*n**4 - 9 + 6/5*n**m + 0*n + 2/3*n**3. Factor v(f).
-2*f**2*(f - 1)**3
Solve 2225/3*b**3 - 8540*b**2 + 85583/3*b + 226981/6 - 125/6*b**4 = 0.
-1, 61/5
Let b(p) = -p**3 + p**2 - p + 1. Suppose -i + 0*i = -6. Let s(k) = -i*k + 6 - 10*k + 19*k**2 - 8*k**2 - 5*k**4 + 4*k**3. Let v(r) = 6*b(r) - s(r). Factor v(n).
5*n*(n - 2)*(n - 1)*(n + 1)
Let v = 16108 - 48316/3. Factor -4/3*l - v*l**2 + 0 - 4/3*l**3.
-4*l*(l + 1)**2/3
Let z = -27 - -29. Factor 54*h**2 - 34*h**z + 7*h**3 + 8*h + 9*h**3 + 4*h**4.
4*h*(h + 1)**2*(h + 2)
Let w(f) be the first derivative of -5*f**6/6 + 3*f**5 - 15*f**4/4 + 5*f**3/3 + 693. Factor w(p).
-5*p**2*(p - 1)**3
Find n such that 0*n**2 - 7/3*n + 1/3*n**3 - 2 = 0.
-2, -1, 3
Let n(g) be the second derivative of 0*g**2 - 2/15*g**3 + 0 - 1/30*g**4 - 9*g. Solve n(m) = 0.
-2, 0
Let s = 1/227 + 1123/2724. Let u(t) be the third derivative of 0 + s*t**4 + 0*t + 1/30*t**5 - 9*t**2 + 4/3*t**3. Factor u(f).
2*(f + 1)*(f + 4)
Suppose 0 = 13*v + 7*v - 40. Factor -7*s**2 - 2*s**2 + 5*s**v - 6*s**2 + 56*s + 24.
-2*(s - 6)*(5*s + 2)
Let j(r) = -11*r**5 - 35*r**4 + 11*r**3 + 30*r**2. Let o(v) = 17*v**5 + 53*v**4 - 17*v**3 - 45*v**2. Let u(m) = 8*j(m) + 5*o(m). Let u(a) = 0. Calculate a.
-5, -1, 0, 1
Factor 42*t**3 + 40 - 186*t - 3*t**4 - 39 - 55 - 63 - 24*t**2.
-3*(t - 13)*(t - 3)*(t + 1)**2
Let c(y) = -y**3 + 14*y**2 + 17*y - 30. Let w be c(15). Suppose 0 = 5*r - 25, w*x + 3*r = 3*x + 9. Solve -1/9*d**3 - 1/3*d - 1/9 - 1/3*d**x = 0.
-1
Suppose -4*v - 330 - 226 = 0. Let d = v + 279/2. Factor d*l + 1/4 - 1/2*l**3 + 3/4*l**4 - l**2.
(l - 1)**2*(l + 1)*(3*l + 1)/4
Let k(h) be the second derivative of -h**4/78 - 2*h**3/3 - 13*h**2 + h - 14. Factor k(m).
-2*(m + 13)**2/13
Let z(p) be the second derivative of 0*p**2 - 39/20*p**5 + 0 + 3/5*p**6 - 22*p + 3*p**4 - 2*p**3 - 1/14*p**7. Factor z(q).
-3*q*(q - 2)**2*(q - 1)**2
Let c(j) be the second derivative of -8/15*j**3 + 16/5*j**2 + 0 + 1/30*j**4 + 2*j. Suppose c(p) = 0. What is p?
4
Let p be (-3)/(258/(-120) + 2). Factor -20*z**4 - 5*z - p*z**2 - 30*z**3 - 5*z**5 - 1144 + 1144.
-5*z*(z + 1)**4
Let j be (-3)/5 - (24/42 + 772/(-420)). Factor j*g - 1/3*g**2 + 1.
-(g - 3)*(g + 1)/3
Let t be ((-141)/235)/((-24)/5). Suppose 1/8*k**2 + 1/4*k + t = 0. Calculate k.
-1
Let y(p) be the third derivative of 1/12*p**4 - 11*p**2 + 0*p + 0 - 1/30*p**5 + 2*p**3. Determine u so that y(u) = 0.
-2, 3
Let f be (2/(-4))/(36/(-288)). Let v(w) be the third derivative of 0*w + 0 - 5*w**2 + 1/20*w**7 - w**3 - 3/40*w**5 - w**f + 1/5*w**6. Solve v(i) = 0 for i.
-2, -1, -2/7, 1
Let d = -1 - -4. Let t(a) = -a**2 + 41*a - 146. Let i be t(37). Let -4*u**i - u**2 + 4*u**2 - d*u**2 + 4 = 0. Calculate u.
-1, 1
Suppose -2*b + 11 = -1. Let x = -2 - -5. Suppose c**4 - b*c**5 + 2*c**3 + 5*c**5 + c**x - c**2 - 2*c**3 = 0. What is c?
-1, 0, 1
Suppose w**3 - 3*w - 28 - 11*w**2 + 10*w - 27*w - 20*w = 0. Calculate w.
-2, -1, 14
Let t(r) be the third derivative of -r**7/210 - 2*r**6/15 + 97*r**5/60 - 41*r**4/6 + 14*r**3 + 250*r**2. Let t(w) = 0. Calculate w.
-21, 1, 2
Factor 24 + 25/4*l**4 - 110*l + 101*l**2 + 115/2*l**3.
(l + 4)*(l + 6)*(5*l - 2)**2/4
Let a(c) be the second derivative of 19*c**6/165 + 17*c**5/110 - 20*c**4/33 + 4*c**3/33 - 31*c + 5. Let a(t) = 0. Calculate t.
-2, 0, 2/19, 1
Let f(i) = -5592*i**4 + 3855*i**3 - 723*i**2 - 7*i + 5. Let y(k) = k**4 + 2*k**3 - k**2 + k + 1. Let q(z) = -f(z) - 3*y(z). Let q(d) = 0. What is d?
-2/23, 2/9, 1/3
Factor 0 + 4*m - 1462*m**2 - 3 + 1461*m**2.
-(m - 3)*(m - 1)
Factor -62*o - 72*o - 32*o + 124*o - o**3 + 43*o**2.
-o*(o - 42)*(o - 1)
Let z(n) be the third derivative of 9*n**8/448 + 3*n**7/70 - n**6/32 - 3*n**5/20 - n**4/8 - 4*n**2 + 11*n. Solve z(m) = 0.
-1, -2/3, 0, 1
Let u be (2 - (-6 - -4)) + 96. Let a = 100 - u. Factor -6/17*j**2 + a - 2/17*j - 6/17*j**3 - 2/17*j**4.
-2*j*(j + 1)**3/17
Determine y so that 2/9*y**2 + 16/3 - 20/9*y = 0.
4, 6
Factor 1/4*y**3 + 3*y + 11/4*y**2 - 1/4*y**5 + 1 - 3/4*y**4.
-(y - 2)*(y + 1)**3*(y + 2)/4
Let h(a) = -23*a**2 - 24*a - 34. Let u(f) = 66*f**2 + 73*f + 103. Let d(n) = -17*h(n) - 6*u(n). Factor d(p).
-5*(p + 2)*(p + 4)
Let t(n) = -10*n**3 - 24*n**2 - 20*n - 6. Let h(u) = 21*u**3 + 47*u**2 + 39*u + 13. Let v(b) = 4*h(b) + 10*t(b). Factor v(m).
-4*(m + 1)*(m + 2)*(4*m + 1)
Let l(a) = a**2 - 23*a + 47. Let r be l(21). Factor r*q**4 - q**5 + 5 - 10*q**2 + 10*q**3 + 3*q**5 - 5*q - 5*q**5 - 2*q**5.
-5*(q - 1)**3*(q + 1)**2
Let a be 267/2937 + 57/99*1. Find k, given that -1/3*k**4 + 4/3*k**2 + 8/3*k + 0 - a*k**3 = 0.
-2, 0, 2
Let p(g) = 351*g**2 - 233*g + 36. Let y(h) = -353*h**2 + 232*h - 36. Let n(x) = 4*p(x) + 5*y(x). Determine a so that n(a) = 0.
6/19
Let f = 121/6 - 39/2. Let b(u) be the second derivative of -6*u + f*u**2 + 0 + 1/3*u**3 + 1/18*u**4. Let b(g) = 0. Calculate g.
-2, -1
Let h be 5 - ((-117)/(-45) - (2 - 4)). Factor 2/5*a**3 + 2/5*a**4 - h*a**2 - 2/5*a**5 + 0 + 0*a.
-2*a**2*(a - 1)**2*(a + 1)/5