3 - 32. Let f be (1/m)/1*-3. Find c such that 1/3*c**3 - f + 1/3*c**2 - 1/3*c = 0.
-1, 1
Let j(v) be the second derivative of -v**6/900 + v**5/50 - 3*v**4/20 - 2*v**3/3 + 23*v. Let o(g) be the second derivative of j(g). Solve o(y) = 0 for y.
3
Let z(o) = -4*o**2 + 20. Suppose 3*h = 2*c - c + 10, -4*h + 4 = c. Let t(r) = -8*r**2 + 41. Let w(m) = c*t(m) + 9*z(m). Factor w(y).
-4*(y - 2)*(y + 2)
Let n = 17 - 9. Let y = 1 + n. Solve -15*m + 8 + y*m**5 - 5 + 0 + 6*m**3 - 15*m**4 + 18*m**2 - 6*m**4 = 0.
-1, 1/3, 1
Let k(s) be the first derivative of -s**6/1440 - s**5/160 + 5*s**3/3 + 20. Let l(f) be the third derivative of k(f). Factor l(c).
-c*(c + 3)/4
Let d(x) be the second derivative of -x**9/3024 + x**7/280 + x**6/180 + 23*x**3/6 - 5*x. Let g(j) be the second derivative of d(j). Factor g(n).
-n**2*(n - 2)*(n + 1)**2
Let t be (2/(-8))/((-8)/96). Suppose -i + t*i = 6. Factor 0*o**2 + o**2 + 8*o - 9*o**2 + 2*o**i.
2*o*(o - 2)**2
Suppose -42*v = -30*v - 37*v + 125. Factor 4/9*g + 2/9*g**4 - 2/9*g**v - 10/9*g**2 + 2/3*g**3 + 0.
-2*g*(g - 1)**3*(g + 2)/9
Let j = 51 + -46. Suppose -5*c - 2 = -u - 16, -j*u - 16 = 2*c. Find q, given that 32/11*q - 8/11 + 18/11*q**c = 0.
-2, 2/9
Let u(s) be the second derivative of 2/5*s**5 + 0*s**2 - 1/15*s**6 + 1/6*s**4 - 4/3*s**3 + 29*s + 0. Determine g so that u(g) = 0.
-1, 0, 1, 4
Let w(i) be the second derivative of -i**4/12 + 13*i**3 - 565*i. Factor w(s).
-s*(s - 78)
Suppose -q + 6*q - 127 = -2*v, 2*v - 5*q - 117 = 0. Factor 65 - 5*x + 2*x**3 - v - x.
2*(x - 1)**2*(x + 2)
Let k(v) be the first derivative of 0*v**2 + 26/85*v**5 + 2/51*v**3 - 4/17*v**4 - 2/17*v**6 + 0*v + 38. Suppose k(d) = 0. Calculate d.
0, 1/6, 1
Let i(s) = 3*s + 8. Let p be i(-2). Factor -37*z**p - 8*z**4 - 2*z**3 - 2 - z**4 - 31*z**3 - 15*z.
-(z + 1)*(z + 2)*(3*z + 1)**2
Suppose -57*q = -82*q + 75. Let u(j) be the second derivative of -1/45*j**q + 0 + 1/150*j**5 + 1/30*j**4 + 6*j - 1/5*j**2. Factor u(n).
2*(n - 1)*(n + 1)*(n + 3)/15
Let j(g) be the second derivative of 75/14*g**2 - 2*g - 5/7*g**3 + 1/28*g**4 + 0. Determine p so that j(p) = 0.
5
Let z(l) = l + 4. Let c(t) = -t - 4. Let d(s) = -5*c(s) - 4*z(s). Let n be d(-2). Suppose -13/2*b**2 + 2*b + n + 5/2*b**3 = 0. What is b?
-2/5, 1, 2
Let d(v) be the second derivative of v**7/280 + v**6/120 - v**5/20 - 7*v**3/2 - 47*v. Let y(u) be the second derivative of d(u). Factor y(f).
3*f*(f - 1)*(f + 2)
Let d(l) = -12*l**2 - 945*l + 237. Let h be d(-79). Let 1/4*w**3 + 1/4*w + h - 1/2*w**2 = 0. What is w?
0, 1
Let g(n) be the first derivative of -10*n**6/21 - 128*n**5/35 - 67*n**4/7 - 208*n**3/21 - 24*n**2/7 + 271. Let g(d) = 0. Calculate d.
-3, -2, -1, -2/5, 0
Let z(x) be the second derivative of -50*x**2 + 0 - 1/12*x**4 - 10/3*x**3 - 42*x. Suppose z(k) = 0. Calculate k.
-10
Suppose 71 + 49 = 4*b. Suppose b = -9*k + 19*k. Factor 1/2*c**k + c + 0 - 3/2*c**2.
c*(c - 2)*(c - 1)/2
Suppose -6*s + 60 = -30. Factor 8*b**2 - 1 - 9 + s*b - 13*b**2.
-5*(b - 2)*(b - 1)
Let b(n) be the second derivative of n**10/90720 + n**9/22680 - n**8/20160 - n**7/3780 + 3*n**4/4 - 28*n. Let f(r) be the third derivative of b(r). Factor f(s).
s**2*(s - 1)*(s + 1)*(s + 2)/3
Let -17193*f**5 + 12*f**4 - 22*f**3 - 64*f**2 - 36*f - 2*f**2 + 17195*f**5 - 2*f**4 = 0. What is f?
-6, -1, 0, 3
Let s(x) = x - 5. Let a be s(6). Suppose 2*v = 4*k - 3*v - a, 0 = -2*v + 6. Solve 8*j**3 - 8*j + 4*j**4 - 6*j**2 + 6*j**2 - k = 0.
-1, 1
Suppose 17*w - 12 = 14*w. Determine y so that 6*y**3 + 2*y**4 + w*y**2 - 539 + 539 = 0.
-2, -1, 0
Let u(k) = -k**4 - k**3 + k**2 + k - 1. Let j(f) = -2*f**4 + 3*f**3 + 11*f**2 + 3*f - 3. Let m(q) = j(q) - 3*u(q). Let m(x) = 0. Calculate x.
-4, -2, 0
Let j(q) be the first derivative of -q**5/15 + q**4/3 - 2*q**3/3 - 3*q**2 - 14. Let p(v) be the second derivative of j(v). Factor p(o).
-4*(o - 1)**2
Suppose m = -4, -3*m = 4*u - 8*m - 244. Let c be 2 - (u/18 + -2). Factor -c*w - 2/9*w**2 - 8/9.
-2*(w + 2)**2/9
Let s(c) be the first derivative of -3*c**4/8 - 35. Determine w so that s(w) = 0.
0
Suppose -d - 29 = -5*o - 2*d, -5*d - 5 = 0. Let c = o + -40/7. Factor 0 - 4/7*s + c*s**2.
2*s*(s - 2)/7
Let n be (-2 + -1)*36/(-54). Suppose -10 = -3*t + q, -q - n*q - 20 = -4*t. Solve -1/4*d**t - 1/4 + 1/2*d = 0 for d.
1
What is b in 60*b - 17*b**5 - 35*b**5 + 188*b**3 + 17*b**5 + 60*b**4 - 63*b**3 - 250*b**2 + 40 = 0?
-2, -2/7, 1, 2
Let w = -57 - -57. Let t(s) be the third derivative of 1/360*s**6 + w + 0*s**4 + 5*s**2 + 0*s + 1/90*s**5 + 0*s**3. Factor t(r).
r**2*(r + 2)/3
Let t(j) be the third derivative of 16/33*j**3 + 1/1155*j**7 + 0 + 0*j**6 - j**2 + 0*j**4 - 4/165*j**5 + 0*j. Factor t(r).
2*(r - 2)**2*(r + 2)**2/11
Let o be (2*2)/(1 + -12 + 18). Factor -2/7*a - 2/7*a**2 + 0 + o*a**3.
2*a*(a - 1)*(2*a + 1)/7
Let o be 1/12*50 + 6/(-36). Let g be 1/15*-6*(-1 - o). Find x such that 0*x + 2/11*x**g - 2/11 = 0.
-1, 1
Let s be 0/(-2 + -1) + 2. Let y be (32 - s) + (-16)/8. Factor 2*c**4 + 3*c**2 + 30*c - 2*c**3 - y*c - 5*c**2.
2*c*(c - 1)**2*(c + 1)
Let s(o) be the third derivative of o**7/945 - 23*o**6/540 + 19*o**5/45 - 53*o**4/27 + 136*o**3/27 - 93*o**2. Factor s(n).
2*(n - 17)*(n - 2)**3/9
Let l(s) be the third derivative of 0*s**6 + 0*s + 0*s**4 + 1/1575*s**7 - 6*s**2 + 0*s**5 + 0*s**3 + 0. Solve l(t) = 0.
0
Let g(b) be the third derivative of -b**8/840 + b**7/420 + b**6/180 - b**5/60 + 4*b**3/3 + 11*b**2. Let k(t) be the first derivative of g(t). Factor k(d).
-2*d*(d - 1)**2*(d + 1)
Let c = -54 + 59. Suppose -c*b**3 - 4*b - 17*b + 8*b**3 - 18*b**2 = 0. What is b?
-1, 0, 7
Suppose 0 = 114*g - 117*g - 27. Let o be 2*5/((-30)/g) + -3. Solve o + 0*f**2 + 0*f - 2/13*f**4 + 2/13*f**3 = 0 for f.
0, 1
Let j(u) be the third derivative of -u**5/240 + 13*u**4/96 + 7*u**3/12 - u**2 + 110*u. Factor j(b).
-(b - 14)*(b + 1)/4
Let x be 0/(-832) + (1 - (-2)/(-6)). Factor -x*n + 0 - 1/3*n**2.
-n*(n + 2)/3
Let w = -20/61 + 1034/549. Suppose -5*r = -2*r - 9. Suppose -4/9*g**2 + 0*g - w*g**r - 14/9*g**4 + 0 - 4/9*g**5 = 0. Calculate g.
-2, -1, -1/2, 0
Let 433*a**4 - 40*a**5 - 8*a**3 - 210*a**4 - 187*a**4 = 0. Calculate a.
0, 2/5, 1/2
Let x be (-1 - (-66)/42)/(6/42). Let k(m) be the first derivative of -2/5*m**5 + 0*m + 0*m**2 + 0*m**3 - m**x - 3. Factor k(w).
-2*w**3*(w + 2)
Let s(i) = 1. Let a be 6/(-15) + (-8)/5. Let m be 4/6 + (-544)/24. Let f(z) = -z**2 + 2*z - 11. Let r(o) = a*f(o) + m*s(o). Factor r(n).
2*n*(n - 2)
Let w(g) be the first derivative of -g**3/2 - 15*g**2/2 + 33*g/2 + 186. Determine t so that w(t) = 0.
-11, 1
Let w = 47257/30 + -1576. Let v = w - -7/6. Determine x, given that v - 4/5*x**2 + 7/5*x = 0.
-1/4, 2
Let x(a) = -a**4 + 2*a**2 - a - 1. Let v(q) = -3*q**4 + 40*q**3 + 222*q**2 + 403*q + 229. Let w(i) = v(i) - 5*x(i). Suppose w(j) = 0. Calculate j.
-13, -3, -1
What is v in -24/19 + 2/19*v**2 + 2/19*v = 0?
-4, 3
Let v(g) = 3*g**2 + 7*g - 3. Let a(i) = i. Let b(k) = 3*a(k) - v(k). Let h(o) = 14*o + 11*o - 24*o. Let c(t) = -b(t) - 4*h(t). Factor c(u).
3*(u - 1)*(u + 1)
Let d be ((-2)/4)/(4*11/(-528)). Suppose -d*v - 4 = -8*v. Factor -2*z**3 - 11/2*z**v - 1/4*z**4 - 9/4 - 6*z.
-(z + 1)**2*(z + 3)**2/4
Let m(k) = 3*k**4 + 45*k**3 - 54*k**2 - 45*k + 48. Let q(z) = z**2. Let u(o) = -m(o) - 3*q(o). Find s, given that u(s) = 0.
-16, -1, 1
Let k = 5/44 + 205/132. Suppose k*p - 4/3*p**2 - p**3 + 2/3 = 0. Calculate p.
-2, -1/3, 1
Let t(x) be the second derivative of -17*x + 0 + 1/12*x**4 + 1/2*x**2 - 1/84*x**7 + 5/12*x**3 - 1/15*x**6 - 1/10*x**5. Suppose t(s) = 0. Calculate s.
-2, -1, 1
Let i(j) be the second derivative of -j**7/14 - 3*j**6/10 - 3*j**5/20 + 3*j**4/4 + j**3 - 5*j + 1. Determine f so that i(f) = 0.
-2, -1, 0, 1
Let b(z) be the first derivative of z**4/54 + 4*z**3/27 + z**2/3 + 6*z - 21. Let v(c) be the first derivative of b(c). Determine q, given that v(q) = 0.
-3, -1
Factor 0*x**2 - 9/7*x**3 + 12/7*x + 0 + 3/7*x**4.
3*x*(x - 2)**2*(x + 1)/7
Let g(c) = 17*c**4 + 2*c**3 - 9*c**2 + 6*c + 6. Let n(x) = 48*x**4 + 5*x**3 - 26*x**2 + 17*x + 17. Let k(q) = -17*g(q) + 6*n(q). Find o such that k(o) = 0.
-3, -1, 0
Find n such that -2/13*n + 4/13*n**2 - 4/13 + 2/13*n**3 = 0.
-2, -1, 1
Let f(q) = q**2 - 13*q + 1. Let a(b) = 11*b**2 - 93*b - 134. Let n(s) = -a(s) + 6*f(s). Determine v so that n(v) = 0.
-4, 7
Suppose 292 =