, -2, -1
Let n(j) be the third derivative of j**8/140 + 6*j**7/175 + 13*j**6/200 + 3*j**5/50 + j**4/40 - 16*j**2 + 2*j. Factor n(w).
3*w*(w + 1)**2*(2*w + 1)**2/5
Let j(u) = -50*u**4 - 116*u**3 - 92*u**2 - 24*u - 2. Let d(y) = 0*y**3 - 3*y**3 + 2*y**3. Let v(z) = -4*d(z) - j(z). Determine g, given that v(g) = 0.
-1, -1/5
Let v be 7*28/49 + 0/2. Factor 0*g - 2/13*g**5 + 8/13*g**2 + 0*g**3 + 0 - 6/13*g**v.
-2*g**2*(g - 1)*(g + 2)**2/13
Let w = 9896938/555 - 53495/3. Let t = w + -2/37. Factor 0 + t*q**3 + 3/5*q**2 + 0*q.
3*q**2*(q + 1)/5
Let t = -88 - -94. Let j(d) = -2*d**2 + 12*d. Let z be j(t). Find n such that 1/5 - 1/5*n**4 + 2/5*n**3 - 2/5*n + z*n**2 = 0.
-1, 1
Let r be (0 - 1)/(((-21)/28)/3). Suppose -75*f**2 + 84*f - 12*f**4 + 56*f**2 + 59*f**2 + r*f**5 - 24*f**3 + 36 = 0. What is f?
-1, 3
Let l(g) be the first derivative of 841*g**3/3 + 116*g**2 + 16*g - 72. Factor l(w).
(29*w + 4)**2
Let r = 1/50 - -1/200. Let h(q) be the third derivative of 6*q**2 + 1/4*q**4 - r*q**6 + 0 - 1/20*q**5 + 0*q + 0*q**3. Factor h(i).
-3*i*(i - 1)*(i + 2)
Let l(q) = -q + 31. Let z be l(13). Let v = z + -18. Let -1/3*r**3 + 0*r + v*r**2 + 0 = 0. What is r?
0
Factor 76*v**2 + 2/3*v**4 + 46/3*v**3 + 272/3 + 424/3*v.
2*(v + 2)**3*(v + 17)/3
Let d(g) be the second derivative of 0 + 0*g**2 - 1/28*g**4 + 3*g + 1/7*g**3. Factor d(s).
-3*s*(s - 2)/7
Let u(y) be the first derivative of y**4/4 - y**3/3 + 2*y - 1. Let w be u(0). Determine j, given that -4 - 4*j**2 + 5 + 3*j**w = 0.
-1, 1
Factor 60*y + 9*y + 58*y + 16 + 361*y**2 + 25*y + 0.
(19*y + 4)**2
Let n(m) be the third derivative of -m**5/150 + 9*m**4/10 + 86*m**2. Factor n(f).
-2*f*(f - 54)/5
Suppose 0 = -31*v + 32*v. Suppose v = -0*n + 6*n. Factor -2/3*r**3 - 2/3*r**4 + 0*r + n + 4/3*r**2.
-2*r**2*(r - 1)*(r + 2)/3
Let m(u) = -11*u + 68. Let x be m(6). Let f(g) be the first derivative of -2*g - 2/3*g**x + 3 + 2/9*g**3. Factor f(n).
2*(n - 3)*(n + 1)/3
Let j be (-1)/((-60)/(-14)) - 30/(-120). Let c(s) be the third derivative of 0*s + 0*s**3 - 8*s**2 + 1/10*s**5 - j*s**6 + 0 - 1/6*s**4. Factor c(b).
-2*b*(b - 2)*(b - 1)
Let m(w) be the second derivative of -w**4/20 + 11*w**3/5 - 363*w**2/10 + 31*w + 2. What is c in m(c) = 0?
11
Determine i, given that 136/3*i**2 - 74/3*i - 10/3*i**3 - 52/3 = 0.
-2/5, 1, 13
Let g(o) be the second derivative of o**4/4 + 178*o**3 + 47526*o**2 - 8*o - 53. Solve g(j) = 0.
-178
Let b(j) = j**5 - j**4 - j**2 - j + 1. Let k(x) = 27*x**5 + 40*x**4 - 4*x**3 - 4*x**2 - 4*x + 4. Let h(i) = 4*b(i) - k(i). Factor h(c).
-c**3*(c + 2)*(23*c - 2)
Let h(z) be the first derivative of z**8/1176 + z**7/980 - z**6/630 + 5*z**3/3 + 34. Let b(w) be the third derivative of h(w). Factor b(k).
2*k**2*(k + 1)*(5*k - 2)/7
Let q = -117 + 1289/11. Let w = -58 - -642/11. Factor q*l**3 + 2/11*l + 0 + w*l**2.
2*l*(l + 1)**2/11
Let a be (-238)/(-51) - (-8)/6 - 3. Let -1/2*g**2 - 1/2*g**a + 0 + g = 0. What is g?
-2, 0, 1
Factor -230*c**4 + 16*c**4 + 40*c + 9*c**4 - 390*c**3 - 197*c**2 - 35*c**5 - 82*c**2 + 59*c**2.
-5*c*(c + 2)**3*(7*c - 1)
Let z(y) be the second derivative of y**6/6 + 15*y**5/4 + 95*y**4/4 + 365*y**3/6 + 75*y**2 - 721*y. Factor z(k).
5*(k + 1)**2*(k + 3)*(k + 10)
Let n(h) be the first derivative of h**5/10 + 5*h**4/8 - 4*h**3/3 - 12*h**2 + 31. Factor n(k).
k*(k - 3)*(k + 4)**2/2
Let w be ((-20)/24)/(7/(-42)). Let a(o) be the second derivative of -1/60*o**w + 0*o**2 + 1/9*o**4 - 2/9*o**3 - o + 0. Find c such that a(c) = 0.
0, 2
Let y = 33 + -29. Find i, given that 1028*i - 11*i**y + 12*i**3 + 3*i**4 - 1026*i + 2*i**5 - 8*i**2 = 0.
0, 1
Let q = 124 - 154. Let h be (-16)/(-48) + (-8)/q. Suppose 0*g - 6/5*g**2 - 3/5*g**3 + 0 + 6/5*g**4 + h*g**5 = 0. What is g?
-2, -1, 0, 1
Let s(w) be the second derivative of -9*w**5/100 - w**4/10 + 4*w**3/15 - 2*w + 38. Factor s(v).
-v*(3*v - 2)*(3*v + 4)/5
Let v(l) be the third derivative of -7*l**6/270 - 88*l**5/45 - 817*l**4/18 + 1444*l**3/27 + 18*l**2 + 2. Factor v(j).
-4*(j + 19)**2*(7*j - 2)/9
Solve -4*r**3 + 21*r**4 - 59*r**4 + 18*r**4 + 14*r**2 + 24 + 18*r**4 + 40*r = 0 for r.
-2, -1, 3
Let m(o) be the second derivative of o**8/1344 - o**7/252 - o**6/144 + o**5/12 - 23*o**4/12 - 2*o. Let p(k) be the third derivative of m(k). Factor p(x).
5*(x - 2)*(x - 1)*(x + 1)
Let b(p) be the third derivative of 1/3*p**3 - 3/8*p**4 - 1/30*p**5 + 3/40*p**6 + 0*p + 5*p**2 + 0. Let b(q) = 0. Calculate q.
-1, 2/9, 1
Suppose 2*m - 2 - 6 = 0. Let v be 0 - -6*1/2. Factor 2*l**3 + 3*l + 4*l**m - 5*l**v + 1 - 5*l**2 + 0.
(l - 1)**2*(l + 1)*(4*l + 1)
Let r be 4 + (-18)/(-15)*(-10)/3. Let f be (r + -1)*-9 - (-640)/(-160). Solve 1/2 - d**3 + 1/2*d**4 + 1/2*d**f + 1/2*d - d**2 = 0 for d.
-1, 1
Suppose -2*n + u = 2*n - 12, -4*n = 2*u - 12. Let g(v) be the first derivative of 0*v + 0*v**2 + 4/33*v**n - 7 + 1/22*v**4 - 2/55*v**5. Let g(x) = 0. What is x?
-1, 0, 2
Suppose 5445*t - 24 = 5421*t. Determine z, given that -7/3*z - t - 2/3*z**2 = 0.
-3, -1/2
Let w = 1/3227 - -3223/12908. Let p be 3/(1/2 - -1). Find y such that -w*y**p - 1/2*y - 1/4 = 0.
-1
Let -58/3*r + 0 + 2/3*r**2 = 0. What is r?
0, 29
Let h(n) be the third derivative of 0*n**3 + 0*n - 1/30*n**6 - n**2 + 0 + 2/3*n**4 + 0*n**5. Factor h(j).
-4*j*(j - 2)*(j + 2)
Let -2/5*z - 2/5*z**5 - 6/5*z**4 + 12/5*z**2 - 6/5 + 4/5*z**3 = 0. Calculate z.
-3, -1, 1
Let u(f) = f**2 + 7*f - 6. Let o be u(-8). Suppose -o*t = -3*t + 2. Suppose 3*w - t*w**3 + 2*w - 3*w = 0. Calculate w.
-1, 0, 1
Let y(t) be the second derivative of t**7/210 - 3*t**6/50 + t**5/5 - t**4/5 - 2*t + 6. Factor y(z).
z**2*(z - 6)*(z - 2)*(z - 1)/5
Let f(g) be the second derivative of -g**4/8 + 55*g**3 - 9075*g**2 - 203*g. Factor f(x).
-3*(x - 110)**2/2
Let b = 2856 - 2854. Factor 2/7*g**b + 0*g + 0.
2*g**2/7
Let h(c) be the first derivative of c**3 + 18*c**2 - 84*c + 83. Factor h(j).
3*(j - 2)*(j + 14)
Let m(g) = 3*g**4 + 7*g**3 + 25*g**2 - 13*g - 48. Let l(t) = 2*t**4 + 4*t**3 + 13*t**2 - 7*t - 24. Let d(j) = -5*l(j) + 3*m(j). Factor d(f).
-(f - 3)*(f - 2)*(f + 2)**2
Factor 200*r**3 - 52*r**4 + 5*r**5 + 66*r**2 + 243*r - 28*r**2 - 54 - 209*r**2 - 171*r**2.
(r - 3)**3*(r - 1)*(5*r - 2)
Suppose 6*g = 7*g - 143. Find z such that -300*z**5 - 10 + 340*z**4 + g*z + 172*z**3 - 324*z**2 - 6 - 15*z + 0 = 0.
-1, 1/3, 2/5, 1
Let g(v) be the first derivative of -v**7/3360 - v**6/720 + 17*v**3/3 + 27. Let k(f) be the third derivative of g(f). Determine h, given that k(h) = 0.
-2, 0
Let -2*a**3 + 82*a + 12254*a**2 + 112 - 12146*a**2 + 140*a = 0. What is a?
-1, 56
Let n(k) be the second derivative of k**6/10 - 12*k**5/5 - 17*k**4/4 + 15*k - 3. Find g such that n(g) = 0.
-1, 0, 17
Let y(j) be the first derivative of 33 + 9*j**2 + 13/2*j**3 + 6*j + 3/10*j**5 + 9/4*j**4. What is x in y(x) = 0?
-2, -1
Let o(a) = 9*a**3 + 12*a**2 + 9*a. Let w(i) = 10*i**3 + 13*i**2 + 10*i. Let l(r) = -7*o(r) + 6*w(r). Factor l(u).
-3*u*(u + 1)**2
Factor -9/4*w - 1/4*w**2 - 2.
-(w + 1)*(w + 8)/4
Let s(y) be the second derivative of 5*y**4/12 - 25*y**3/6 + y - 66. Factor s(b).
5*b*(b - 5)
Let o be (-30)/((-10)/2) - 3. What is d in -2*d + 2*d + 16*d**o + 2*d**2 - d**5 - 2*d**4 - 15*d**3 = 0?
-2, -1, 0, 1
Factor -27/2*c - 1/4*c**2 + 55/4.
-(c - 1)*(c + 55)/4
Let w(y) = y**2 - 8*y + 10. Let g be w(7). Find t, given that -25*t - t**g - 27*t + t**2 + 54*t = 0.
-1, 0, 2
Let l(m) be the third derivative of 0*m**4 + 2*m**2 + 0*m + 0*m**3 + 0 + 1/1155*m**7 + 0*m**6 - 1/330*m**5. Factor l(u).
2*u**2*(u - 1)*(u + 1)/11
Factor 0 - 3/2*b**4 - 12*b + 1/2*b**5 - 3*b**3 + 14*b**2.
b*(b - 2)**3*(b + 3)/2
Let g be (-3 - -3) + 93/45. Let l = g - -23/15. Factor -3/5*a**4 - 12/5*a - 12/5*a**3 - 3/5 - l*a**2.
-3*(a + 1)**4/5
Let w = 126 + -123. Let t be (-3)/(-6) + 4*1. What is y in 1/2*y**2 + t + w*y = 0?
-3
Factor -12 + 4*k**4 - k**2 + 2*k**2 + 16*k**3 - 9*k - 7*k + 7*k**2.
4*(k - 1)*(k + 1)**2*(k + 3)
Let g(f) be the second derivative of 5*f**4/8 - 3*f**3/4 - 3*f**2/2 + 229*f. Solve g(q) = 0.
-2/5, 1
Let a(h) = 9*h**5 - 16*h**4 - 33*h**3 + 5*h**2 - 13. Let k(c) = 2*c**5 - 4*c**4 - 8*c**3 + c**2 - 3. Let o(q) = -6*a(q) + 26*k(q). Factor o(r).
-2*r**2*(r + 1)**2*(r + 2)
Let y(s) = -2*s**2 + 8*s + 22. Let h(w) = w - 1. Let m(n) = -6*h(n) - y(n). Factor m(i).
2*(i - 8)*(i + 1)
Let f(d) = -4*d - 7. Let y be f(-2). Solve -18*v + 2