21)/(-98). Find o such that -50/7*o**3 + 0*o + 0 - r*o**5 + 0*o**2 + h*o**4 = 0.
0, 5
Let j(f) = 19*f - 853. Let g = -2397 + 2442. Let h be j(g). Suppose 0*m**3 + 0*m**h + 2/5*m**5 + 0*m + 4/5*m**4 + 0 = 0. What is m?
-2, 0
Let y(w) be the second derivative of -w**5/4 - 35*w**4/3 + 5*w**3/6 + 70*w**2 + 2038*w. Let y(c) = 0. Calculate c.
-28, -1, 1
Suppose 8*b - 4*b = 4, -66 = -5*v + 4*b. Factor 43*y**2 - 15*y - 39*y**2 - 21*y - v - 26.
4*(y - 10)*(y + 1)
Let b be ((-44)/(-8) - 5)/(2/96). Suppose 7*u + 5*u - b = 0. Factor -4 + 27*m - 23*m - 12 + u*m**2.
2*(m - 2)*(m + 4)
Let c(y) be the first derivative of 0*y + 2/15*y**5 - 1/27*y**6 - 1/9*y**4 - 188 + 0*y**3 + 0*y**2. Factor c(r).
-2*r**3*(r - 2)*(r - 1)/9
Let t(f) = f**3 + 41*f**2 - 297*f - 703. Let b be t(-47). Factor -1/2*s**b + 2*s - 3/2.
-(s - 3)*(s - 1)/2
Let y = 2117/24 - 2099/24. Factor 1/4*d**2 - 1/2 - 3/4*d**3 + 1/4*d**4 + y*d.
(d - 2)*(d - 1)**2*(d + 1)/4
Let f be 18*(50/(-15))/(-2). Factor r + 2*r**2 - 36*r**3 - f*r**3 + 67*r**3.
r*(r + 1)**2
Let c(g) = -2*g**2 + 27*g - 108. Let h be c(6). Let k be 5/30 + (2 - (-3)/h). Factor -1/6 + 0*v + 1/6*v**k.
(v - 1)*(v + 1)/6
Let u be (-1 + 17/10)*78/96. Let w(n) be the third derivative of -7/120*n**7 - u*n**6 + 0 - 5/24*n**4 + 0*n**3 + 0*n + 16*n**2 - 3/5*n**5. Solve w(a) = 0.
-5, -2/7, 0
Let i(m) be the first derivative of -3*m**4/4 - 17*m**3 + 267*m**2/2 + 315*m - 6547. Solve i(q) = 0 for q.
-21, -1, 5
Suppose 4*t - 12 = 3*n - 13, -5*n + 23 = 4*t. Suppose -14 = -2*k - 3*q - 11, -t*q = -5*k + 17. Factor -1/5*i - 2/5*i**2 + 2/5 + 1/5*i**k.
(i - 2)*(i - 1)*(i + 1)/5
Suppose -141*t**3 - 4*t**5 - 184*t**3 + 5*t - 127*t**4 + 8*t - 59*t**2 + 17*t + 113*t**3 = 0. What is t?
-30, -1, 0, 1/4
Suppose 8*l - 17/2 + 1/2*l**2 = 0. What is l?
-17, 1
Solve -99/4*y**3 - 189 + 3/4*y**5 - 597/4*y**2 - 288*y + 9/4*y**4 = 0.
-3, -2, 7
Let g(c) be the first derivative of -51470*c + 0*c**3 + 12*c**2 - 162 + c**3 + 51443*c. Factor g(i).
3*(i - 1)*(i + 9)
What is g in 5/3*g + 8/3*g**2 - 14/3 + 1/3*g**3 = 0?
-7, -2, 1
Let u(f) = -14*f + 16. Suppose -75 = -4*k - 71. Let m be u(k). Let 1 + 7/4*y + 1/2*y**m - 1/4*y**3 = 0. What is y?
-1, 4
Suppose 0 = -6*m + 1222*m - 3648. What is l in 13/3*l**m - 1/3*l**2 + 1/3*l**4 + 0 - 13/3*l = 0?
-13, -1, 0, 1
Let y(r) be the second derivative of -5/4*r**4 - 3/20*r**5 - 2 + 17*r + 0*r**2 - 3/2*r**3 + 1/10*r**6. Determine m so that y(m) = 0.
-1, 0, 3
Let o = 367 - 1827/5. Suppose o - 26/15*l + 2/15*l**2 = 0. Calculate l.
1, 12
Let k(n) be the second derivative of n**4/12 - 113*n**3/3 + 225*n**2/2 - 23*n - 95. Factor k(u).
(u - 225)*(u - 1)
Let q(m) be the second derivative of 5*m**7/42 - 47*m**6/6 + 87*m**5/4 + 695*m**4/12 - 440*m**3/3 - 450*m**2 - 13*m + 10. Find r such that q(r) = 0.
-1, 2, 45
Suppose -27 = 16*p - 20*p - 3*u, u + 11 = 2*p. Let l be ((-5)/p)/(20/(-16) + 0). Find j, given that 2/3*j**2 - l*j - 4/3 = 0.
-1, 2
Let c(k) be the second derivative of -21/8*k**3 + 5/16*k**4 - 1/80*k**5 + 49/8*k**2 - 9*k + 1. Factor c(r).
-(r - 7)**2*(r - 1)/4
Let x be (-42 + 29174/696)/(2/(-6)). Factor -15/4 + 4*c - x*c**2.
-(c - 15)*(c - 1)/4
Factor -1073/4*o**2 + 1/4*o**3 + 0*o + 0.
o**2*(o - 1073)/4
Let a = 1 - 1. Suppose -3*p + a*p + 11 = j, -j = -4*p + 10. Factor -j*h - 4*h**2 + 10*h**2 - 5*h**2.
h*(h - 2)
Let n = 159 - 159. Suppose 9 = -3*k + 21. What is c in 0*c**2 - k*c + c + n*c**2 - 4*c**2 - c**3 = 0?
-3, -1, 0
Let p(y) = -y**3 + 5*y**2 + 14*y - 6. Let i be p(7). Let l be (-18)/i*-1 + 3. Suppose 19*r + l*r**3 - r**3 - 3*r - 3*r**3 = 0. Calculate r.
-2, 0, 2
Determine f so that -286*f**2 - 25 - 147*f**3 - 168*f**3 - 102*f**3 + 321*f**3 - 160*f - 9*f**4 = 0.
-5, -1/3
Let h(c) be the first derivative of -c**6/1440 - c**5/32 - 7*c**4/48 + 53*c**3 - 65. Let u(r) be the third derivative of h(r). Solve u(w) = 0.
-14, -1
Let v be ((-129)/15 - 1)*-15. Let z be 36/15*240/v. Suppose 3/7*k**2 + 6/7*k**3 + 0 + 3/7*k**z + 0*k = 0. Calculate k.
-1, 0
Let y(o) be the first derivative of o**6/39 - 36*o**5/65 + 29*o**4/13 + 144*o**3/13 - 59*o**2/13 - 396*o/13 - 5042. Determine z so that y(z) = 0.
-2, -1, 1, 9, 11
Let z(n) be the second derivative of 0*n**2 - 7/8*n**3 - 16*n - 3/80*n**5 + 0 + 1/2*n**4. Let z(h) = 0. Calculate h.
0, 1, 7
Let q(j) be the second derivative of j**6/15 - j**5/2 - 31*j**4/24 + 11*j**3/3 - 3*j**2 - 4173*j. Factor q(f).
(f - 6)*(f + 2)*(2*f - 1)**2/2
Let s be -2*1 - (14 - (-905)/25). Let t = -45 - s. Factor -16/5*n - 64/5*n**2 + 0 + t*n**3.
4*n*(n - 2)*(9*n + 2)/5
Let a(u) = -u**3 + 6*u**2 + u + 10. Let k be a(6). Suppose -8*x**3 - 15*x**2 + 44*x**4 + 23*x**5 + k*x + 20 - 49*x**2 - 31*x**5 = 0. Calculate x.
-1, -1/2, 1, 5
Suppose -96*u + 90*u = -4*p - 56, 0 = 5*p + 5*u - 80. Determine j so that 2*j**3 - 19/10*j + 8/5*j**p - 5*j**2 + 17/5 - 1/10*j**5 = 0.
-2, -1, 1, 17
Suppose 465*k - 528*k + 126 = 0. Find j, given that 2 - 16/3*j**4 + 49/3*j + 103/3*j**k + 8/3*j**3 = 0.
-2, -1/4, 3
What is f in -1316*f - 176*f**2 - 4*f**3 + 4837 - 10900 + 4103 = 0?
-35, -7, -2
Let z(s) be the first derivative of 5/12*s**4 - 8 + 0*s**3 + 17*s + 0*s**2. Let g(l) be the first derivative of z(l). Suppose g(i) = 0. Calculate i.
0
Let x(a) be the second derivative of -1/18*a**5 + 5/54*a**4 - 2/3*a**2 + 5/27*a**3 + 26*a + 1/135*a**6 + 1. Solve x(t) = 0.
-1, 1, 2, 3
Solve 30/7 - 2/7*q**3 - 46/7*q + 18/7*q**2 = 0 for q.
1, 3, 5
Let g(o) be the first derivative of -o**6/60 + 9*o**5/40 - 5*o**4/6 + o**3 + 191*o - 51. Let q(c) be the first derivative of g(c). Factor q(x).
-x*(x - 6)*(x - 2)*(x - 1)/2
Let z(q) be the first derivative of q**6/72 + 3*q**5/8 + 5*q**4/3 + 2*q**3/3 + q**2 + 77. Let n(x) be the third derivative of z(x). Let n(h) = 0. What is h?
-8, -1
Let w = 710 - 3538/5. Suppose -2912 = -692*c - 764*c. Factor 3/5*o**c - w*o + 0.
3*o*(o - 4)/5
Suppose -49*b + 208 = -36*b. Suppose 3*a**2 + 15 - 2*a**2 + 0*a + 3*a**2 - b*a + 1 = 0. Calculate a.
2
Determine n so that 497664 + 15485*n**2 - 2999250*n + 403668 - 7*n**3 - 13*n**3 - 152487 = 0.
1/4, 387
Suppose -4*p + 4*x - 48 = 0, -3*p - 11438*x + 11435*x + 48 = 0. Find m such that 72/5 - 36/5*m + 4/5*m**p = 0.
3, 6
Suppose 85*z - 45 = 43 - 3. Let o(p) be the first derivative of -z - 8*p - 12*p**2 + 14/3*p**3. Factor o(r).
2*(r - 2)*(7*r + 2)
Suppose 0 = 2*c - 321*n + 326*n + 25, -3*c = 3*n + 15. Factor 10*k**3 + c + 19/2*k**2 + 0*k + 1/2*k**4.
k**2*(k + 1)*(k + 19)/2
Let p(y) be the second derivative of -9*y**5/20 - 73*y**4/4 - 132*y**3 - 120*y**2 + 1332*y. Suppose p(b) = 0. What is b?
-20, -4, -1/3
Solve 2/3*w**2 + 4089800/3 + 5720/3*w = 0.
-1430
Let k be (-23)/92 - 34/(-8). Factor -3*y**2 + 2 + 3*y**5 - 34*y + 40*y + 3*y**k - 2 - 9*y**3.
3*y*(y - 1)**2*(y + 1)*(y + 2)
Suppose 0 = 23*l - 3 - 43. Let g(b) = 3*b**2 + b - 12. Let z be g(l). Factor -1/7*u + 2/7*u**z + 0.
u*(2*u - 1)/7
Let m(t) = -7*t + 63. Let d be m(9). Solve -20*y**4 - 129*y + 25*y**2 + 35*y**3 + 99*y + d*y**2 = 0 for y.
-1, 0, 3/4, 2
Suppose -4*f - 963*l = -960*l + 8, 0 = f + l + 4. Factor 42/5*p**2 - 6/5*p**f + 0*p**3 + 0 - 36/5*p.
-6*p*(p - 2)*(p - 1)*(p + 3)/5
Let z(b) be the second derivative of 6*b**3 + 57*b - 20*b**2 + 1/3*b**4 + 0. Suppose z(f) = 0. Calculate f.
-10, 1
Suppose -2*c = 17 - 117. Let n = 4 + -2. Find u, given that 4*u**3 - c*u + 50*u + u**3 + 5*u**n = 0.
-1, 0
Factor -120*l**3 - 35*l + 4*l**4 + 993 - 110*l**2 - 5*l**5 - 993 - 54*l**4.
-5*l*(l + 1)**3*(l + 7)
Let j(m) = 33*m**3 + 65*m**2 - 238*m + 20. Let g(l) = -34*l**3 - 67*l**2 + 239*l - 23. Let z(c) = 4*g(c) + 5*j(c). Find w such that z(w) = 0.
-4, 1/29, 2
Let u(n) = 2*n**2 + 8*n - 8. Let s(a) be the third derivative of a**4/24 + a**2 + 1. Let x(r) = 28*s(r) - 2*u(r). Solve x(l) = 0.
-1, 4
Factor -44*a**3 + 350*a - 45*a**2 - 38*a**3 - 65*a**3 + 142*a**3.
-5*a*(a - 5)*(a + 14)
Suppose 4*n - 89 = n + 5*x, -4*x + 134 = 3*n. What is v in -4*v**5 - 12*v**2 - n + 23 + 12*v**4 + 15 + 4*v**3 = 0?
-1, 0, 1, 3
Suppose -3*t - 4*b = -69, 5*t = -0*b - b + 115. Factor -t*n - 11 - 30*n**2 - 10*n + 7 + 74 + 5*n**3 - 12*n.
5*(n - 7)*(n - 1)*(n + 2)
Let o be (2/1 - (-13 + 9)) + -142. Let m be (-34)/o*1488/28. Determine i so that 12/7 - 12/7*i**5 - 24/7*i**4 + 60/7*i + m*i**2 + 33/7*i**3 = 0.
-2, -1, -1/2, 2
Suppose -10*j - 141 = -13*j. Suppose -4*w + i + 0*i = -j, -3