
Let w(t) = t**2 - 1. Suppose 9*d - 87 = -96. Let y(i) = -2*i**2 - 3*i + 5. Let h(m) = d*y(m) - 3*w(m). Let h(v) = 0. Calculate v.
1, 2
Let w(z) = 5*z**2 - 12*z + 2. Let u be w(-5). Suppose -u = -3*b + 257. Find n such that 144*n**2 - b*n**2 + n + 4*n**4 - n = 0.
-1, 0, 1
Let m(d) be the first derivative of d**4/2 - 6*d**3 + 20*d**2 - 24*d - 965. Factor m(y).
2*(y - 6)*(y - 2)*(y - 1)
Let x = -8137/999 + 411/37. Let t(g) be the first derivative of -18/5*g**5 - x*g**3 + 0*g + 4/9*g**2 + 13/2*g**4 - 15. Factor t(w).
-2*w*(w - 1)*(9*w - 2)**2/9
Let p(j) = -j**2 - 58*j + 319. Let k be p(5). Let h(m) be the second derivative of 4/3*m**3 + 0 - 7*m + 2*m**2 + 1/3*m**k. Suppose h(q) = 0. What is q?
-1
Factor 27/2 + 109/2*z**2 + 2*z**4 + 93/2*z + 47/2*z**3.
(z + 1)**2*(z + 9)*(4*z + 3)/2
Let f = 6510 - 6508. Let i(j) be the second derivative of -21*j - 10/21*j**3 + 0 + 1/21*j**4 + 8/7*j**f. Factor i(k).
4*(k - 4)*(k - 1)/7
Let o(c) be the first derivative of -4*c**5/3 + 17*c**4/3 + 52*c**3/3 - 102*c**2 + 72*c + 5259. Solve o(t) = 0 for t.
-3, 2/5, 3
Let p(b) = 19*b + 477. Let i be -105 + 85 - (1 + (4 - 0)). Let w be p(i). Factor 3/4*c**w + 27/2*c + 243/4.
3*(c + 9)**2/4
Let d(b) be the first derivative of -5/4*b**4 + 0*b + 162 + 10/3*b**3 - b**5 + 0*b**2. Find k, given that d(k) = 0.
-2, 0, 1
Let z(a) = a**2 - 22*a - 21. Let u be z(-1). Let 14*g + 12*g - 361*g**2 + 29*g + 356*g**u = 0. What is g?
0, 11
Let z = -89 - 7. Let s be 3/(-12) + (-344)/z. Determine g so that -s - 8/3*g + 2/3*g**2 = 0.
-1, 5
Let i be ((-9 + 9)/21)/(-3). Determine j, given that 0 - 8/15*j**3 + 2/15*j**4 + i*j + 0*j**2 = 0.
0, 4
Let f = 3/1052213 - -5261059/2104426. Determine n so that 0 + 9/2*n**3 - n - 7/2*n**5 - 5/2*n**2 + f*n**4 = 0.
-1, -2/7, 0, 1
Let p(f) be the first derivative of -16*f + 2/3*f**6 + 8*f**4 - 18*f**2 - 8/3*f**3 + 24/5*f**5 + 115. Let p(h) = 0. Calculate h.
-4, -1, 1
Factor 3/5*p**3 + 504/5 - 54/5*p**2 - 453/5*p.
3*(p - 24)*(p - 1)*(p + 7)/5
Let w = -610 + 625. Find s such that 5*s**3 + 10 + 12*s**2 - 4*s**4 + 4*s**3 - w - s**3 - 16*s - 11 = 0.
-1, 2
Let n(a) = 6*a**2 + a. Let t(q) = 57*q**2 + 41*q + 8. Let y(d) = 14*n(d) - 2*t(d). Factor y(u).
-2*(u + 2)*(15*u + 4)
Let c(h) = h - 6. Let x be c(9). Suppose 0 = 3*p + 5*u - 16 + 11, -2*p + 16 = -x*u. Factor 0*i**4 - 5/2*i**p + 0*i**2 - 5/2*i + 5*i**3 + 0.
-5*i*(i - 1)**2*(i + 1)**2/2
Let b(o) = 31*o - 31. Let d be -4 - (-7 + 0) - 2. Let p be b(d). Solve 6/7*y - 3/7*y**2 + p = 0.
0, 2
Factor 0 - 134*m + 1/4*m**2.
m*(m - 536)/4
Let x be -35*38/(-1197) + (-2)/3. Let i(f) be the third derivative of 0 + 1/540*f**6 - 1/27*f**4 + 16*f**2 + 0*f + x*f**3 - 1/90*f**5. Factor i(h).
2*(h - 3)*(h - 2)*(h + 2)/9
Let t = 10576 + -10574. Let p(v) be the second derivative of 0 + 17*v + 1/9*v**4 - 1/3*v**3 - 2/3*v**t + 1/10*v**5. Determine x so that p(x) = 0.
-1, -2/3, 1
Let x(t) = 51 + 18 + 83*t + 19 - 94*t. Let s be x(8). Solve -12/5*w**3 - 16/5*w**2 + s*w**4 + 2/5*w**5 - 6/5*w + 0 = 0.
-1, 0, 3
Let h(k) = 40*k + 15604. Let q be h(-390). Determine v, given that -10/3*v**2 - 45/2*v**3 + 15/2*v + 5/3 + 50/3*v**q = 0.
-2/5, -1/4, 1
Let h(g) = 34781 - 3*g**2 - 34781 + 0*g**2 - 4*g + g**3. Let o be h(-1). Factor o*x**3 - 6/7*x**2 + 0 + 2/7*x**4 + 4/7*x.
2*x*(x - 1)**2*(x + 2)/7
Let o(w) be the second derivative of w**6/80 - 123*w**5/160 - 133*w**4/32 + 41*w**3/16 + 99*w**2/4 - w - 989. Solve o(g) = 0 for g.
-3, -1, 1, 44
Factor 273*q - 223587/2 - 1/6*q**2.
-(q - 819)**2/6
Suppose 359*g - 313*g = 138. Let o(l) be the second derivative of -1/5*l**5 + 0*l**g - 9*l + 0 + 0*l**4 + 0*l**2. Let o(b) = 0. Calculate b.
0
Suppose 116*x + 106*x - 1332 = 0. Let q(w) be the second derivative of 0 + 5*w + 0*w**2 + 0*w**4 + 1/10*w**x + 0*w**3 + 1/14*w**7 - 3/10*w**5. Factor q(z).
3*z**3*(z - 1)*(z + 2)
Let v = 151 + -117. Suppose -20*g + v*g = 70. Factor 0 + 1/3*i**g - 4/3*i**4 + 0*i - 2/3*i**2 + 5/3*i**3.
i**2*(i - 2)*(i - 1)**2/3
Factor -2523/2*q**2 - 177/2*q**4 - 2697/2*q**3 + 0 + 0*q - 3/2*q**5.
-3*q**2*(q + 1)*(q + 29)**2/2
Let c(j) = 10*j + 52. Suppose -4*r = 5*o - 5, 0 = -5*r - 2*o + 3*o - 30. Let v be c(r). Factor 3/7*p**4 - 9/7*p + 9/7*p**3 + 3/7*p**v - 6/7.
3*(p - 1)*(p + 1)**2*(p + 2)/7
Let u = -1129/636 - -322/159. Factor -13*l**2 + u*l**5 - 5/2 - 5/2*l**4 + 17/2*l**3 + 37/4*l.
(l - 5)*(l - 2)*(l - 1)**3/4
Factor -2*n**3 - 15*n**5 - 61*n**3 - 1894*n**2 + 8*n**4 - 6*n + 1927*n**2 + 43*n**4.
-3*n*(n - 1)**3*(5*n - 2)
Let n = -33 + 38. Suppose 4*m - 22 = -5*r, -5*m + 64 = n*r + 39. Find b, given that 12/7*b - 4/7 - 12/7*b**r + 4/7*b**3 = 0.
1
Let 1/2*l**2 + 149/2 - 75*l = 0. What is l?
1, 149
Let l(f) be the second derivative of -87*f**5/140 + 59*f**4/14 - 62*f**3/7 + 12*f**2/7 + 4990*f. Solve l(o) = 0.
2/29, 2
Let p be ((-32)/(-56))/((-8)/(-28)). Factor -20 + 62*f - 205*f + 56*f + p - 27*f**2.
-3*(f + 3)*(9*f + 2)
Let q(h) be the second derivative of -h**5/10 - 13*h**4/2 - 38*h**3/3 - 7*h. Factor q(b).
-2*b*(b + 1)*(b + 38)
Let p(b) be the third derivative of 0 + 1/30*b**5 - b**4 - 13/3*b**3 - 4*b**2 - b. Factor p(a).
2*(a - 13)*(a + 1)
Suppose -99*z + 118 + 131 = 51. Factor -10/3*q + q**z + 1.
(q - 3)*(3*q - 1)/3
Let f(n) be the first derivative of -7*n**6/30 + n**5/4 + 3*n**4/4 - 5*n**3/6 - n**2 - 169*n + 27. Let i(v) be the first derivative of f(v). Factor i(y).
-(y - 1)**2*(y + 1)*(7*y + 2)
Let r be (-2 - (-848)/432)*-54. Factor -16/7*h - 4/7*h**r - 12/7.
-4*(h + 1)*(h + 3)/7
Let n(x) be the first derivative of x**4/16 - 103*x**3/36 - 335*x**2/12 - 100*x/3 + 7498. Factor n(t).
(t - 40)*(t + 5)*(3*t + 2)/12
Let u(y) be the third derivative of -y**5/105 - 41*y**4/21 + 688*y**3/21 - y**2 + 4209*y. Factor u(v).
-4*(v - 4)*(v + 86)/7
Suppose -3*a - 12 = 0, -51*t - 4*a - 30 = -53*t. Let c(r) be the first derivative of -16/3*r**3 - t*r**2 - 1/2*r**4 - 33 + 0*r. Let c(f) = 0. What is f?
-7, -1, 0
Let d be ((-438)/(-1)*(-32)/(-40))/(96/64). Suppose -64/5 - d*z**2 + 126*z**3 + 98/5*z**4 + 504/5*z = 0. Calculate z.
-8, 2/7, 1
Factor 1/3*m**3 + 20 - 1/3*m**2 - 32/3*m.
(m - 5)*(m - 2)*(m + 6)/3
Let f(w) be the third derivative of -w**6/240 + 9*w**5/40 + 7*w**4/12 + 665*w**2. Factor f(u).
-u*(u - 28)*(u + 1)/2
Let p(n) be the third derivative of 2*n**5/75 - 773*n**4/60 + 193*n**3/15 + 6*n**2 - 2*n - 159. Factor p(r).
2*(r - 193)*(4*r - 1)/5
Let f(j) be the second derivative of 2*j**6/75 + j**5/25 - j**4/5 - 2*j**3/15 + 4*j**2/5 - 196*j + 2. Factor f(z).
4*(z - 1)**2*(z + 1)*(z + 2)/5
Factor 80*o**2 + 5*o**3 + 24*o - 450 + 29*o + 23*o - 31*o.
5*(o - 2)*(o + 3)*(o + 15)
Let b(l) be the second derivative of 1/18*l**4 + 20/3*l**2 + 28*l - 7/3*l**3 - 5. Factor b(x).
2*(x - 20)*(x - 1)/3
Let u(i) = 4*i**3 - 3*i**2 - 9*i + 5. Let j(b) = -7*b**3 + 7*b**2 + 17*b - 9. Let x(d) = 3*j(d) + 5*u(d). Let z be x(5). Factor -3*r**2 - z + 97 - 44 + 3*r**4.
3*r**2*(r - 1)*(r + 1)
Let v(z) = -41*z - 187. Let q be v(-9). Let -48*w**3 + 665*w**2 + 562*w**3 - 135 + q*w**4 + 1131*w**3 + 308*w**4 - 405*w - 260*w**2 = 0. What is w?
-3, -3/7, 1/2
Let a be ((-286)/88)/((-3)/936). Solve 9*m**3 - a*m + 24 + 6*m**2 + 978*m - 3*m**4 + 0*m**4 = 0.
-2, 1, 2
Let g(z) be the first derivative of z**6/2 - 8*z**5/5 - 13*z**4/4 + 22*z**3/3 + 12*z**2 + 537. Find t such that g(t) = 0.
-4/3, -1, 0, 2, 3
Let g be -5 + (2 + (-174)/12)/(51/(-34)). Factor 14/3*v**2 + 0 + 4/3*v + g*v**4 + 2/3*v**5 + 6*v**3.
2*v*(v + 1)**3*(v + 2)/3
Factor -q**2 + 2*q**2 + 1110*q + 2*q**2 + 104522 - 36153 + 34306.
3*(q + 185)**2
Let o(l) be the second derivative of -l**4/78 - 8*l**3/13 + 25*l**2/13 + 2645*l. Find d, given that o(d) = 0.
-25, 1
Let d(a) = 0*a**2 + a + 0*a + a**3 + a**2. Let m(c) be the first derivative of -c**4/4 - 16*c**3/3 - 11*c**2/2 + 252. Let q(t) = -4*d(t) + m(t). Factor q(k).
-5*k*(k + 1)*(k + 3)
Let i = -17877 + 17880. Let l(p) be the first derivative of -4*p**i + 1/2*p**4 + 9*p**2 - 8*p + 4. Find s such that l(s) = 0.
1, 4
Let f(i) be the first derivative of -3/80*i**6 - 21/2*i**2 - 8 + 3/16*i**4 - 1/40*i**5 + 1/4*i**3 + 0*i. Let g(v) be the second derivative of f(v). Factor g(o).
-3*(o - 1)*(o + 1)*(3*o + 1)/2
Let n(r) be the first derivative of r**8/280 - r**7/75 + 2*r**5/75 + 19*r**2 + 15. Let a(k) be the second derivative of n(k). Determine h, given that a(h) = 0.
-2/3, 0, 1, 