 88*j - 22*j = 78 - 78. Let n(x) be the second derivative of -3/2*x**2 + 23*x + 1/4*x**4 + 0 + j*x**3. Solve n(s) = 0.
-1, 1
Let t = -85 - -87. Solve 0*m**2 + 5*m - 1280 - 165*m - 5*m**t + 0*m**2 = 0.
-16
Let j be (540/32)/15 - (-1)/(-4)*4. Let v(i) be the first derivative of 1/12*i**3 + 5/16*i**2 - j*i**4 - 1/48*i**6 - 1/10*i**5 - 30 + 1/4*i. Factor v(w).
-(w - 1)*(w + 1)**3*(w + 2)/8
Let z(l) be the first derivative of l**4/108 + 13*l**3/27 + 169*l**2/18 + 11*l + 35. Let x(o) be the first derivative of z(o). Factor x(g).
(g + 13)**2/9
Suppose -9*k + 5616 = 27*k. Solve -k*w - 2*w**2 - w**2 - 1245 - 783 = 0.
-26
Factor -84*f + 932 + 110*f - 5*f**2 + 748 - 414*f - 442*f.
-5*(f - 2)*(f + 168)
Let l = 1698971 - 1698960. Factor -77*h**2 + 13/2*h**3 + 119/2*h + l.
(h - 11)*(h - 1)*(13*h + 2)/2
Suppose 6 = -0*f + 4*f - 3*h, 17 = 5*f + h. Suppose -f*g - 2*w + 36 = 0, g - 25 = 4*w + 1. Factor 16*y**3 - 33 + 54*y - 21 - 18*y**2 - g*y**3.
2*(y - 3)**3
Suppose 3*b + 4*j = -34, b + 3*j + 0 = -8. Let a(t) = 30*t + 423. Let q be a(b). Let -4/7*m**q + 8/7*m**2 - 4/7*m + 0 = 0. What is m?
0, 1
Let g(k) be the first derivative of -2846498*k**5/5 - 1420863*k**4 - 2827418*k**3/3 + 4764*k**2 - 8*k - 3022. Suppose g(c) = 0. Calculate c.
-1, 2/1193
Let b(t) be the third derivative of -t**7/840 - 131*t**6/480 - 171*t**5/80 - 637*t**4/96 - 127*t**3/12 + t**2 - 9*t + 4. Determine g, given that b(g) = 0.
-127, -2, -1
Let z = 91 - 97. Let q be (4/z)/(6/(-36)). Factor -2854 - 3*a**2 + 2854 - q*a + 2*a**2.
-a*(a + 4)
Let v = -109626/7 - -15662. Factor 8/7*o + 4/7*o**2 - 4/7*o**4 - v*o**3 + 0.
-4*o*(o - 1)*(o + 1)*(o + 2)/7
Let a(k) be the first derivative of -8*k**2 - 14/3*k**3 + 17/2*k**4 + 66 + 8*k - 3*k**6 + 6/5*k**5. Find b such that a(b) = 0.
-1, 2/3, 1
Let o(z) = -z**2 - 16*z - 9. Let i be o(-6). Factor -12 - 49*f**4 - 68*f + i*f**3 - 39*f**2 + 117*f**3 + 0*f**3.
-(f - 3)*(f - 1)*(7*f + 2)**2
Let f(m) be the first derivative of 2*m**3/3 - 3*m**2/2 + 16*m + 36. Let v(d) = -d**2 + 2*d - 8. Let n(o) = -4*f(o) - 9*v(o). Factor n(j).
(j - 4)*(j - 2)
Suppose -725*v**3 - 10*v**4 + 1873*v + 1415*v**2 + 15*v**4 + 777*v - 505*v = 0. What is v?
-1, 0, 3, 143
Let t(h) be the second derivative of -h**4/3 + 1864*h**3/3 - 434312*h**2 - 758*h + 1. Let t(i) = 0. What is i?
466
Let u be (-7)/(-14) - 75/(-6). Factor 4*s**4 + 5*s**5 - 6*s**4 - u*s**4 + 15*s**2 - 10*s + 5*s**3.
5*s*(s - 2)*(s - 1)**2*(s + 1)
Let p = -284 + 362. Factor -28*m**4 + 102*m**3 + p*m**3 - m**5 - m**5 - 32*m**4 + 7*m**5.
5*m**3*(m - 6)**2
Let 16*k**2 - 820 + 37*k + 6*k**2 - 17*k**2 - 852*k = 0. Calculate k.
-1, 164
Let m(o) = -o**2 + 1. Let z(g) = -7*g**2 + 1116*g - 155677. Let v(q) = -5*m(q) + z(q). Factor v(l).
-2*(l - 279)**2
Let n = 64 + -52. Factor -7*l**2 - 42 - 80*l - 43 + n*l**2 + 0*l**2.
5*(l - 17)*(l + 1)
Let y = 66622 - 333108/5. Let z = -21 - -23. Factor -4/5*g + 6/5 - y*g**z.
-2*(g - 1)*(g + 3)/5
Suppose -1140 = 46*l - 8*l. Let f be (31 + l)*4/3. Factor -f*c**3 + 2/3 + 3*c + c**2.
-(c - 2)*(c + 1)*(4*c + 1)/3
Let j = 79940050/309 - 258705. Let v = j - -1/309. Factor -26/3*t**2 - 8/3 + 8*t - v*t**4 + 4*t**3.
-2*(t - 2)**2*(t - 1)**2/3
Suppose -36*t - 12*t + 15*t = -11*t + 28*t. Determine p so that 2/9*p**4 - 16/9*p**3 + 0*p + 14/9*p**2 + t = 0.
0, 1, 7
Suppose 1387*u - 6228 - 38156 = 0. Determine l, given that -4/3*l**2 - u - 100/3*l = 0.
-24, -1
Let v(w) be the first derivative of -5*w**3/3 - 75*w**2/2 + 170*w - 1147. Determine t, given that v(t) = 0.
-17, 2
Suppose -14*f + 62*f = 48. Let y(l) = 2*l**3 - 3*l**2 + 47*l - 46. Let g be y(f). Factor 2/9*z**2 + g*z - 2/9.
2*(z - 1)*(z + 1)/9
Let v(f) be the third derivative of -4/3*f**3 + 2/15*f**5 - 1/120*f**6 + 0*f + 1/24*f**4 - 4*f**2 + 3. Determine w, given that v(w) = 0.
-1, 1, 8
Suppose -5*p + 5*o + 25 = 0, -13*p - 4*o = -16*p + 13. Factor -56 + 3*d**2 + 13 - 3*d + p.
3*(d - 4)*(d + 3)
Let f(z) be the first derivative of -5*z**7/42 - z**6/6 - 108*z - 97. Let x(o) be the first derivative of f(o). Determine y, given that x(y) = 0.
-1, 0
Let y(t) be the first derivative of -t**6/9 + 232*t**5/45 - 97*t**4/6 + 212*t**3/27 + 8*t**2 + 2776. Suppose y(n) = 0. What is n?
-1/3, 0, 1, 2, 36
Let v(i) = -i**3 - 32*i**2 - 31*i. Let m be v(-31). Factor 0*p + 1/4*p**3 + 0*p**2 + 1/4*p**4 + m.
p**3*(p + 1)/4
Let n be 6/22 + ((-320)/(-55) - 6). Let f = -19973/11 + 1816. Let -2/11 - n*g**4 + 1/11*g + f*g**2 - 1/11*g**3 = 0. Calculate g.
-2, -1, 1
Let v(x) = x**3 - 6*x**2 - 4*x - 3. Let s be v(7). Let g = 23 - s. Determine j, given that 5*j**g + 21*j**2 - j**5 + 20*j**4 - 21*j**2 + 24*j**3 = 0.
-3, -2, 0
Factor -12*h**4 - 4*h**5 - h**5 - 32*h**4 + 13*h**3 + 57*h**3 + 19*h**4.
-5*h**3*(h - 2)*(h + 7)
Factor 3954*q**2 - 3954 - 9*q**3 + 585*q + 584*q + 6*q**3 + 588*q - 1754*q.
-3*(q - 1318)*(q - 1)*(q + 1)
Let y(u) be the first derivative of -38*u**5/25 - 18*u**4/5 - 2*u**3 + 2*u**2/5 - 1420. Factor y(c).
-2*c*(c + 1)**2*(19*c - 2)/5
Factor -13/5*m**3 + 538/5*m + 453/5*m**2 + 72/5.
-(m - 36)*(m + 1)*(13*m + 2)/5
Let s(h) be the first derivative of h**6/15 - 46*h**5/5 + 57*h**4/5 + 1133. Determine x, given that s(x) = 0.
0, 1, 114
Let g(y) be the second derivative of 7*y**3 + 15/2*y**2 - 3/4*y**4 + 0 - 4*y. Determine l, given that g(l) = 0.
-1/3, 5
Let a(q) be the second derivative of -2*q**7/105 - 7*q**6/15 - 49*q**5/15 - 121*q**2/2 + 148*q. Let w(l) be the first derivative of a(l). Solve w(i) = 0.
-7, 0
Let s = 115 - 111. Let q = -288 - -288. Let -3/5*w + w**2 + q - 1/5*w**s - 1/5*w**3 = 0. What is w?
-3, 0, 1
Let a be (-14)/(-4)*5309/37163. Find r, given that 0 - 2*r**2 - 3*r**3 + 4*r + a*r**4 + 1/2*r**5 = 0.
-2, 0, 1, 2
Let d(l) be the first derivative of l**3/9 - 5*l**2/6 - 3888. Factor d(h).
h*(h - 5)/3
Let p(r) = r**3 - 45*r**2 + 209*r - 357. Let m be p(40). Factor 4/7*j**m + 0*j**2 - 2/7 - 4/7*j + 2/7*j**4.
2*(j - 1)*(j + 1)**3/7
Solve 1/6*f**4 - 29*f + 33/2 + 46/3*f**2 - 3*f**3 = 0.
1, 3, 11
Let l(d) = -4*d**2 + 48*d - 115. Let x(s) = -s**2 - s - 1. Let c(a) = -l(a) + 5*x(a). Factor c(r).
-(r - 2)*(r + 55)
Let r(v) be the third derivative of 0 + 27/28*v**4 + 19*v**2 + 0*v + 1/140*v**5 + 729/14*v**3. Suppose r(j) = 0. What is j?
-27
Let r(h) be the second derivative of h**6/60 + h**5/10 - 5*h**4/6 - 8*h**3 - 86*h**2 - 9*h + 4. Let m(i) be the first derivative of r(i). What is v in m(v) = 0?
-4, -2, 3
Let q = 1706/11 - 155. Let d be ((-29)/(-58))/(407/222). What is n in -d*n**2 - 1/11*n**3 + 1/11*n + q*n**4 + 2/11 = 0?
-1, 1, 2
Determine z so that -29/3*z - 18 + 1/3*z**3 + 26/3*z**2 = 0.
-27, -1, 2
Let h(z) = 20*z**2 + 2605*z - 2691. Let n(c) = -4*c**2 - 522*c + 538. Let r(p) = -2*h(p) - 11*n(p). Solve r(g) = 0 for g.
-134, 1
Let x = -157 + 143. Let c(l) = -12*l**2 - 24*l + 5. Let v(s) = -34*s**2 - 72*s + 14. Let y(a) = x*c(a) + 5*v(a). What is j in y(j) = 0?
-12, 0
Let y be (16/12)/((-1544)/(-168) - 9). Let o(x) be the third derivative of -1/490*x**y + 0*x**4 + 1/140*x**6 + 0*x**5 + 0*x**3 + 0*x + 0 + 15*x**2. Factor o(c).
-3*c**3*(c - 2)/7
Let z = -7318 + 7321. Let x(n) be the first derivative of n**4 + 29 + 0*n - 1/5*n**5 + n**2 - 5/3*n**z. Determine j, given that x(j) = 0.
0, 1, 2
Let z be (37 - (-6086)/(-170)) + (-7)/((-560)/(-36)). Determine a, given that 0 + 0*a**2 + 0*a + 3/2*a**3 + z*a**4 = 0.
-2, 0
Let q(d) = 2*d**2 + 9*d - 89. Let m(p) = p**2 + 4*p - 45. Let v(i) = -5*m(i) + 3*q(i). Let l be v(4). Factor 2/3*g**l + 0 - 2/3*g.
2*g*(g - 1)/3
Let y(f) be the third derivative of -f**6/30 - 26*f**5/15 - 139*f**4/6 - 76*f**3 + 3*f**2 + 1064. Factor y(a).
-4*(a + 1)*(a + 6)*(a + 19)
Let x(m) be the first derivative of 0*m + 11/24*m**4 + 0*m**2 + 1/3*m**3 + 57 - 1/36*m**6 + 2/15*m**5. Factor x(b).
-b**2*(b - 6)*(b + 1)**2/6
Let f = 146 - 77. What is a in 2*a**4 + 26*a + 19*a**4 + 3*a**5 + 21*a**3 + 0*a**5 - f*a**2 - 29*a - 21*a + 48 = 0?
-4, -1, 1
Let w(j) be the second derivative of -3*j**5/100 + 62*j**4/5 - 7688*j**3/5 - 662*j - 3. Let w(g) = 0. What is g?
0, 124
Suppose -15*d + 8 = -17*d. Let v be 2/d*-6 - -1. Factor 5*r + v*r + 3*r - 6 - 3*r - 3*r**2.
-3*(r - 2)*(r - 1)
Let v(u) = -2*u**2 + 18*u + 3. Let p(m) = 2*m**2 - 16*m - 4. Let s(j) = -3*p(j) - 4*v(j). Factor s(q).
2*q*(q - 12)
Let b(p) be the third derivative of -p**8/30240 + p**7/5670 + p**6/10